
■tmwBmwwnn 

m 






■ill 

FMbghr 1m 

139 BramttnHitSfil 



IqhotRI 



JH Hn 

8f3fi»ffi 



m HUB 

WJBB8B 

80 DM 

ftMHS 

nraB 

EHJ 

Ra? BHHIl 

HBIBWBB 

M m 
Ural 



in 



Outlines 



OF 



ASTRONOMY. 



BY 



ARTHUR SEARLE, A.M., 

ASSISTANT AT HARVARD COLLEGE OBSERVATORY. 










BOSTON: 






G I X N BROTHERS. 






1874. 




• 






Entered according to Act of Congress, in the year 1874, by 

ARTHUR SEARLE, 

In the Office of the Librarian of Congress, at Washington. 



CAMBRIDGE ! 
PRESS OF JOHN WILSON AND SON. 



PREFACE. 



Jo one, probably, would maintain that a student 
who had no intention of attempting to read, speak, 
or write the Greek language, could spend his time 
profitably in committing a Greek grammar to memory; 
methods analogous to this are still sometimes 
employed in the study of science. No practical man, 
however, needs to be told that learning any number of 
scientific facts from books cannot be called the study 
of the subject to which those facts relate, but can only 
be called picking up general information about the sub- 
ject. It is well to have a stock of general information 
about many subjects apart from those which we study 
thoroughly ; but general information can never be exact, 
and its acquisition ought to constitute the recreative, 
not the laborious, part of education. The study of a 

ck grammar written in Latin will improve the stu- 
dent's knowledge of Latin, but will be worthless as a 

ins of teaching him Greek, unless he follows it up 
by practice in reading that language. In like manner, 
the knowledge of any natural science, obtained only 
from a text-book, is scarcely valuable enough to war- 
rant the consumption of much time in committing the 
book to memory, although its statements may be made 
with all the pr<jci>ion attainable by the use of mathe- 



iv Preface. 

matics. The student may derive from it some real 
knowledge of mathematics, but little or none of the 
science which he has professedly been studying. 

Few persons can undertake any serious study of 
astronomy, for want of the necessary appliances. There 
is, indeed, a purely mathematical branch of astronomy, 
which may be thoroughly mastered by the study of 
books alone, aided by actual practice in mathemat 
reasoning. But this theoretical astronomy, as it 
called, is too difficult, except in its mere rudiments, for 
use in general education ; and it is rather a branch 
of mathematics than of natural science, although its 
results are applicable to astronomical work. 

For most students, then, the study of astronomy 
merely means the acquisition of such an amount <>f 
general information about that science as may serve 
to add to the rational interests and pleasures of their 
lives. The present work is accordingly intended rather 
to be read than to be learned by heart. The useful 
mental discipline which can be gained from books 
general information chiefly consists in the practice 
the arts of consulting them as works of reference, 
of correctly interpreting their meaning, and of properly 
estimating their authority. Although this practice can- 
not be extensively carried on at school, it is certainly 
injudicious to bring up young people to regard knowl- 
edge as consisting in the power of passing examinations 
which test only their memories, not their judgments. 

But since these examinations in matters of mere gen- 
eral information are unfortunately in extensive use in 
our schools and colleges, teachers may find it net 
sary, if they use this book at all, to require their pupils 
to prepare parts of it for recitations of the customary 



Preface. v 

kind. To accommodate the book to this use, heavy 
has frequently been employed to call attention to 
subjects on which questions may conveniently be asked ; 
and in the first, or descriptive, portion of the book, the 
3 relating to the subjects which are most impor- 
;. or best suited for recitations, have been numbered 
in heavy type. The sections of the eighth and follow- 
ing chapters are of necessity somewhat closely con- 
nected with each other ; no distinction, therefore, has 
been made between them, and each chapter after the 
nth will probably be studied or read without omis- 
sions, in any manner which may be preferred. No 
ful purpose, however, can be served by learning the 
meaning of azimuth (for example) by heart. If any one 
measures or calculates a few angles of azimuth in the 
course of his daily work, he will never forget what the 
word means ; if he never has occasion to measure 
or calculate an angle of azimuth, why should he remem- 
ber what it is ? It is enough if he knows where to look 
for its meaning and its connection with other astronom- 
ical terms, on any occasion when he may require this 
knowledge. Accuracy does not mean omniscience, and 
indeed the attempt to acquire omniscience is certain to 
result in inaccuracy. 

To facilitate the use of this book as a work of refer- 
ence, its index has been made somewhat extensive, and 
frequent references have been inserted in the text from 
subsequent to preceding sections relating to associated 
the top of each page will be found the num- 
ber of the section to which the first line of the page 
belongs. It may perhaps be found useful, after the 
k has been read, to spend a moderate time in study- 
l it by subjects, with the aid of the index. Its Ian- 



vi Preface. 

guage has been made plain and clear to the best of the 
writer's ability, and perhaps with the result of making 
parts of it tediously diffuse ; but it seemed better to 
run some risk of this kind than to fall into the opposite 
error. Mathematical and technical expressions b 
been avoided, so far as possible, in the first seven chap- 
ters ; and illustrative geometrical figures have been 
replaced by verbal illustrations wherever this seemed 
practicable. For reasons which need not here be dis- 
cussed, many learners acquire little from their early 
mathematical studies except an ^discriminating dislike 
of mathematics in general. Under these circumstances, 
they are disposed to pass over a mathematical explana- 
tion of any subject as hastily as possible, and to attach 
no strictly definite meanings to the terms used in it. 
the manifest detriment of their reasoning faculties. On 
the other hand, students who have some actual work- 
ing knowledge of mathematics may exercise themsel 
profitably in reducing an explanation given in ordinary 
language to a strict mathematical form, and illustrat- 
ing it by geometrical figures of their own drawing, or, 
still better, by solid models of their own construction. 
Whatever they can do for themselves of this kind will 
teach them more, both of mathematics and of the subject 
to which they apply it, than they would gain from ten 
times as much work laid out in merely following the 
demonstrations of their text-books. Other reasons for 
the plan pursued in the present work are that too fre- 
quent references from the text to illustrative figures 
become vexatious to almost all readers, and sometir 
result in making the student better acquainted with the 
figures themselves than with the subjects which they 
are meant to explain. Moreover, an explanation de- 






Preface. vii 

pendent on an illustrative figure cannot conveniently 
be followed by a listener, if it is read aloud ; this, how- 
ever, is a comparatively slight drawback to the use of a 
school-book. As this work may be used by students 
who have never attained any facility in mathematical 
reasoning, or who have lost what they formerly had, the 
small amount of geometry required for the explanation 
of the telescope, and of the rudiments of practical and 
theoretical astronomy, is included in the eighth chap- 
ter, and in those which follow it. Any one who either 
remembers his geometry, or can work it out for himself, 
will be able to find neater methods of proof for the 
propositions employed in the fourteenth chapter than 
those which are there given because they seemed the 
most direct. 

A good way of testing the learner's comprehension 
of any work of general information is to ask him ques- 
tions, the answers to which are not contained in the 
work itself, but may readily be inferred from it. It is 
useless to publish many such questions with the work ; 
because, if the learner knows them in advance, they are 
no longer tests of his knowledge, but only of his indus- 
try. The following questions may serve as specimens 
of the kind just mentioned. They may be useful after 
the whole work has been read ; and the student should 
have the work before him to assist him in answering. 

Why are the apparent paths of solar spots such as 
they are said to be in section 59 ? 

Why ought each successive magnitude of stars to 
include more stars than the preceding magnitude? See 
sections 79, 457. 

At what time of night may we expect that shooting 
stars will be, on the whole, most abundant, on the prin- 



viii Preface. 

ciple that the forward side of a moving object is, on the 
whole, most likely to encounter other objects? 

Why does the Earth's rotation prolong an eclipse of 
the Sun? Does this prolongation happen at all places 
on the Earth from which eclipses of the Sun are ever 
seen ? 

Does the Earth's movement in its orbit shorten or 
lengthen the time of a transit of Venus? of an eclipse 
of the Sun? 

What are the poles of the prime vertical? of the 
equinoctial colure ? 

Why should Paramatta be said in the Almanac to 
be fifteen hours east, rather than nine hours west, of 
Washington ? 

It will also be well to accustom the learner to distin- 
guish accurately between different uses of the same 
word. The following are examples of words used in 
various senses: altitude, aurora, corona, diameter, hemi- 
sphere, horizon, penumbra, phase, umbra. 

Teachers who wish to exercise their pupils in simple 
astronomical calculations will find materials for this 
purpose in the sixteenth chapter. The precessions of 
stars, and hence their approximate proper motions, the 
periods of the synodical revolutions of the planets, the 
relative weights of equal masses at the surfaces of differ- 
ent bodies, and other problems of like character, may 
be studied by the aid of the data contained in this 
work ; but of course some little knowledge of algebra 
and trigonometry must previously be had. 

The only way of enabling a reader to estimate the 
authority of any statement placed before him is to 
accustom him to demand references to original authori- 
ties, and to test the correctness of every statement 



Preface. ix 

whenever he can. This part of education is too often 
neglected ; and grown men sometimes take any thing in 
print for gospel, and at other times are unreasonably 
sceptical. It would be well if readers required refer- 
ences throughout all popular works on science ; but it 
would probably appear pedantic to fill this book with 
citations. Accordingly, it is only in the sixteenth chap- 
ter, which contains distinct statistical statements, that 
authorities are referred to. Care has been taken, how- 
ever, throughout the book, to check, by means of original 
treatises, the statements derived from popular works ; 
and it is hoped that few errors have escaped attention 
in the revision of the text. For the historical portion 
of the book, Delambre has been the chief authority 
consulted. 

The illustrative lithographs have been copied, with 
Professor Winlock's permission, from the series of "As- 
tronomical Engravings from the Observatory of Har- 
vard College/' On consideration, it has been thought 
best not to attempt any representation of nebulae or 
comets. Good representations would be so expensive 
as to add too much to the price of the work ; while ordi- 
nary ones, such as usually appear in popular works on 
astronomy, are of little or no service to the reader. 

The thanks of the author are due to Professor Win- 
lock for occasional assistance in settling doubtful points, 
and for many valuable suggestions. 



CONTENTS. 



CHAPTER I. 
Objects of Astronomy. 



Page 



General notions relating to the size, shape, and movements of the 
Earth. — The ether and its contents. — Celestial and terrestrial ob- 
jects i 

CHAPTER II. 

Properties of Matter. 

Solids, liquids, and gases. — Light and heat. — Chemical differences. 
— Mass 4 

CHAPTER III. 

The Material Universe. 

Scientific and unscientific questions about the universe. — Its apparent 
and its actual structure. — Classes of celestial objects 10 

CHAPTER IV. 

Suns, or Fixed Stars. 

The Sun. — Its atmosphere. — Rotation. — Poles and equator. — Di- 
rect and retrograde movement. — Bulk and mass of the Sun. — Its 
appearance. — Faculas, spots, and prominences. — Number of visible 
stars. — Star magnitudes. — Places of principal stars in the sky. — 
Clusters of stars. — Variable and temporary stars 20 

CHAPTER V. 

Planets. 

General account of the planets. — Real and apparent movement. — 
Laws of nature. — The Earth's rotation. — Pendulum experiments. 



xii Contents. 

Page 

— Plane of the ecliptic. — Orbits. — Kepler's laws. — The Earth. — 

m The Moon. — Mercury and Venus. — The superior planets and their 
satellites 58 

CHAPTER VI. 

Nebulae, Comets, and Meteors. 

Appearance and distribution of nebulae. — Remarkable nebulae. — 
Comets. — Their orbits and appearance. — Their connection with 
meteors. — Meteoric streams. — Sporadic meteors. — Aerolites . . 130 

CHAPTER VII. 

Phbnomi 

Meaning of the words "up M and " down." — The horizon. — The skv. 

— Refraction. — Projection and perspective. — Aurora 1 and other at- 
mospheric phenomena. — The tides. — Apparent movements of the 
stars ; and of the Sun. — The year and its seasons. — Mean time. — 
Sidereal time. — Local time. — The ecliptic and the zodiac. — Ap- 
parent movements of the Moon and of the planets. — Transits, 
occupations, and eclipses 143 

CHAPTER VIII. 
Geometrical Terms. 

Solids, surfaces, lines, and points. — Rectilinear motion and rotation. 

— Distances, angles, and arcs. — Spheres and cones. — Triangles. 

— Normal lines 208 

CHAPTER IX. 
Optical Terms. 

Reflection. — Refraction. — Dispersion. — Prisms, mirrors, and lenses. 

— Formation of images. — Visual angles 220 

CHAPTER X. 

The Telescope. 

The magnifying-glass. — The astronomical refracting telescope. — 
Object-glasses and eye-pieces. — Power of telescopes. — Reflecting 
telescopes. — Spy-glasses and opera-glasses. — Fixed lines in the 
field of a telescope 234 



Contents. xiii 



CHAPTER XI. 

The Spectroscope. 

Page 
Separation of different kinds of light. — Formation of spectra. — Con- 
struction and use of the spectroscope 246 

CHAPTER XII. 

Practical Astronomy. 

The celestial sphere. — Apparent places. — Geocentric and heliocentric 
places. — Azimuth and altitude. — Terrestrial longitude and lati- 
tude. — Right ascension and declination. — Celestial longitude and 
latitude. — Parallax. — Sidereal time. — Aberration. — Mean places. 
— Nodes and apsides. — Anomaly. — The tropical year. — Mean 
time. — The fictitious year 255 

CHAPTER XIII. 

Astronomical Instruments. 

Sundial. — Time-pieces. — Chronograph. — Graduated circles. — Ver- 
niers. — Micrometers. — The sextant. — The transit instrument. — 
The meridian circle. — Altitude and azimuth instruments. — Equa- 
torials 289 

CHAPTER XIV. 

Theoretical Astronomy. 

Forces. — Laws of motion. — Mass. — Gravitation. — Kepler's laws. 
Determinations of mass. — Weight. — Geographical and geocentric 
latitude. — Surveying. — Precession. — Tides 



301 



CHAPTER XV. 

History of Astronomy. 

The ancient astronomers. — Star catalogues. — Variable stars. — Ris- 
ing an 1 ^ett:n^ of stars. — Shape <>i the Earth. — Distance of the 
nd of the Moon. — Astronomy in the middle ages. — Coperni- 
cus Tycho, Kepler. —Galileo, Huygens Picard. — Newton and his 
successors. — Velocity of light — Parallax of Mars and of Venus. 
Parallax of stars. — The calendar. — Cycles. — The nebular hypoth- 
esis 



344 



xiv Contents. 



chapter XVI. 
Notes, References, and Statistics. 



I 



Page 



Titles of books referred to. — Figure and dimensions of the Earth. — 
Latitudes and longitudes of some observatories. — Refraction and 
dip. — Sun's rotation, parallax, dimensions, mass, spots, and heat. 
Number of stars ; data respecting variable and other stars. — Ele- 
ments of planets and of satellites. — Notes relating to subjects men- 
tioned in the previous chapters 3S5 






INDEX 4 ,i 



LIST OF ILLUSTRATIONS. 



In the following List, the letters H. C. O. show that the Plate opposite 
the number of which they stand is copied from the "Astronomical En- 
gravings from the Observatory of Harvard College": — 

Plate Page 

I. The Sun. II. CO 38 

II. Sun Spots. H. C. 38 

III. Three Ellipses 82 

IV. The Moon. H. C. O. 112 

V. Plato (one of the lunar mountains). H. C. O. . . 112 

VI. Jupiter. H. C. 122 

VII. Saturn. H. C. 122 

VIII. Solar Eclipse. H. C. 202 

IX. Umbr.e and Penumbr.-e 208 

X. Distribution of Light at an Equinox . . . 20S 

XL Distribution of Light at a Solstice .... 20S 

XII. Geometrical Figures 208 

XIII. Telescope of the U. S. Naval Observatory, 

Washington 299 



. error in the printing of this edition, Plates IX., X 
ea placed h and 194, Instead of between 

pages 207 ai ,.- number.: Plate* I. and [X. should be- 

about 170. in order to make the explanation of P . ect. 



OUTLINES OF ASTRONOMY. 



CHAPTER I. 



OBJECTS OF ASTRONOMY. 

1. All the countries and oceans about which we learn by 
the study of geography make up the outside of that great 
ball, or globe, eight thousand miles thick, which is called the 
it thousand miles is so great a distance that we 
cannot well understand how great it is without the help of 
some comparison, like this. Suppose that, on some winter 
day, when the ground is covered with damp snow, we roll up 
a snowball a yard thick or more, so as to reach up to the 
waist of a man standing beside it. Let us make this snow- 
ball as round and smooth as possible, and then stick some 
rather small pins into it up to their heads. The heads of 
those pins will stand out as far from the snowball, with respect 
to its size, as the highest mountains in South America or 
India stand out from the Earth. So, too, if we make a little 
hollow in the snowball, just large enough to hold the head of 
a pin, that hollow will go as deep into the snowball as the 
hollows which contain the oceans go into the Earth, and 
deeper than the deepest mines go into it. Of course it would 
be very hard to make a snowball so perfectly round and 
smooth as not to have little lumps and hollows upon it many 
tinv than pin-heads ; and yet, in spite of these little 

5, the ball would look smooth enough to any one 
standing a 4 3 away from it. So, too. the Earth's 

lUSed by its mountains and its valleys, both on 
land and under the sea, is really SO slight in comparison with 

i 



2 Outlines of Astronomy. [Sec. i. 

its size, that we may regard it as a smooth round ball when 
we are considering the whole of it at once. We can now 
understand a little better what is meant when we are told that 
the Earth's diameter is eight thousand miles ; for if a pin's 
head on a ball a yard thick is large enough to represent a 
great mountain on the Earth, we may imagine how small a 
house or even an ordinary hill would be when it was repre- 
sented on the same scale. We see, besides, that the Earth's 
mountains cannot be represented in the right proportion by 
raised figures on a globe or map made on any ordinary scale. 

2. The Earth seems to us to stand still ; but, in fact, it is 
always moving along in much the same way that a ball is 
moving after it has rolled oif the roof of a house and before 
it has come to the ground. Such a ball has at least three 
different kinds of movement at the same time. First, it is 
falling to the ground : but this is not all ; for it does not drop 
directly downwards, as it would if it had been stopped just 
when it came to the edge of the roof and I .in. In- 
stead of this, it has gained some headway by rolling down 
the roof; and while it is falling, this hi irrics it far- 
ther and farther from the house. This is its second kind of 
movement. But besides falling and moving away from the 
house, it goes on rolling in the air just as it did on the r 
This third kind of movement is not so easy to see as the 
others, because it is generally too quick for the eye to foil 
But if we take a rather large and light ball, — like a foot- 
ball, for instance, — place it near the ech^e of a smooth board 
a few feet from the ground, and then tilt the board just enough 
to make the ball roll otT. we shall see that it turns over a little 
while it is falling. This can be seen more plainly if the ball 
is marked in some way ; by pasting pieces of paper upon it, 
for example. 

3. It is seldom that any ball moves in the air without 
having all the kinds of movement just described ; that is, a 
dropping movement, a forward movement, and a rolling 
movement. The Earth is like any other ball in these re- 
spects ; it is always falling, moving on, and rolling. How it 



Sec. 3.] Objects of Astronomy. 3 

can be always falling without being stopped by something 
else, as a falling ball is stopped by the ground, will be ex- 
plained hereafter. Another difference between the Earth 
and a tailing ball is, that what the Earth moves in is not the 
air ; tor the air is really part of the Earth, and goes alon^ 
with it. What the Earth moves in is not known. It is com- 
monly called ether (the Greek word for air), because it is 
thought to resemble air in some respects; but the chief 
reason for believing that there is any such thing as this 
ether is that the light of the sun, moon, and stars takes 
time to come from them to us : and the easiest explanation 
of this is that the light comes to us through ether as sound 
comes through air, or as waves come along the water from 
the sea to the shore. Ether is a name which is also given to 
certain chemical liquids ; but this use of the word has noth- 
ing to do with the other. 

4. We know more of what the ether contains than of what 
it is. Many great globes, more or less like the Earth, are 
moving about in the ether. Some of them are known to be 
vastly larger than the Earth ; others, again, are smaller. Be- 
sides these, the ether contains, as we have reason to think, a 
great deal of material resembling that of which the Earth is 
made, but scattered about instead of being collected together 
in masses. It is all in motion, however, so far as is known. 
All the knowledge we can get of these various contents of the 
ether belongs to the science of astronomy, — which also in- 
cludes so much study of the Earth itself as is useful in mak- 
ing comparisons between it and other objects. For this 
reason, astronomy has much in common with geography, 
geology, chemistry, mechanics, optics, and other sciences. 
But the direct purpose of astronomy is the study of what 
outside of the Earth, and at a great distance from it. 
of this kind is called a celestial object; what 
is part of the Earth, on the other hand, is called terrestrial. 



4 Outlines of Astronomy. [Sec. 5. 

CHAPTER II. 

PROPERTIES OP MATTER. 

5. Every thing which we perceive by means of our senses 
is called matter, when it is spoken of as one thing. But 
when we speak of the separate things which our senses make 
known to us, we call them material objects, or sometimes 
bodies, instead of matter. Material objects are either solids, 
liquids, or gases ; and the same thing may be at different 
times solid, liquid, or gaseous, according to the circum- 
stances in which it is placed. The most familiar example of 
this is furnished by water, which is often seen in the solid 
form of ice or snow, and is known to exist a- although 
its shape cannot be seen when it is in that state; for when 
we see watery vapor, the water is in the form o\ little liquid 
drops, such as those which make up fog or mist. As for 
clouds, they may be made either of crystals of snow or 

or of drops of water which are kept up for a long time by the 
air. just as dust is kept up by it. But besides the liquid 
water Moating in the air, there is al iter 

forming part of the atmosphere itself, which is no more to be 
seen than are the other gases of the atmosph h as 

nitrogen. Steam, too, is a g is while it continues hot enough 
to remain invisible. We see, by the way in which water 
changes from one state to another, that what makes any 
material object solid, liquid, or gaseous, is partly its amount 
of heat, and partly other causes, which are to be learned by 
the study of natural philosophy and chemistry. 

6. Solids, liquids, and gases may all be so hot as to shine, 
or give out light of their own. They are then said to be 
incandescent. An incandescent object may be on fire, as we 
say; but burning and incandescence do not always go to- 
gether. A piece of lime, for instance, shines \ July 



Sec. 6.] Properties of Matter. 5 

when it is exposed to a great heat ; but it does not burn : for 
what is meant by burning is permanent change as well as 
brightness and heat ; and when the lime is cool again, it is 
still lime, as it was before. Melted metals also are often 
incandescent, and yet burn very little, if at all. In fact, few 
metals are commonly considered as combustible. We sel- 
dom see an incandescent gas, unless it is burning, because 
the particles of a gas are usually driven away by heat to some 
cooler place. Every flame is caused by burning gas ; but 
most of the light of a flame is generally due to incandescent 
solid particles in it, not to the incandescence of the gas itself. 
An incandescent gas, whether burning or not burning, usu- 
ally gives out much less light than an equally hot solid or 
liquid. 

7. When any object shines by light of its own, and yet is 
not very hot. we call it phosphorescent instead of incandes- 
cent. Phosphorescence is not so usual a kind of shining as 
incandescence is ; and when a celestial object shines by 
light of its own. we naturally suppose it to be incandescent, 
unless we can discover some proof that it is only phosphores- 
cent. Incandescent and phosphorescent objects are some- 
times called sources of light, or self-luminous bodies. 

8. Many objects shine very brightly, and yet are neither 
incandescent nor phosphorescent. If a piece of polished 
glass or metal, for example, is held in the sunlight, it looks 
very bright when we see it from that particular place towards 
which most of the light that falls on it is reflected. All 
objects, so far as is known, reflect some light, although some 
reflect very little ; and it is by means of this reflected light 
that we see most of the terrestrial and many of the celestial 
objects which are visible to us. Even gases reflect a little 
light Some gases, like chlorine, have a distinct color, which 
enables us to see them : and the mixture of gases which 
makes up the Earth's atmosphere, or the air, as we com- 
monly call it. has a blue tint, which can be seen when we 
look through many miles of it at a time. But if the floating 
solid and liquid matter contained in the air were all removed 



6 Outlines of Astronomy. [Sec. 8. 

from it, it would probably reflect very little li^ht, and would 
scarcely look blue. This blueness of our atmosphere occa- 
sions the appearance which we call the sky, as will be shown 
hereafter. 

9. Any material object may be hot or cold, luminous or 
dark ; and probably, too, may exist under certain circum- 
stances either as a solid, a liquid, or a gas. But there are 
other differences between material objects, which at all 
times distinguish them from each other. A piece of iron, 
for instance, differs in some respects from a piece of 1 
whether the metals are solid or liquid, incandescent or 
dark and cold. Differences of this sort are called chemical 
differences. These chemical differences are accompanied by 
differences in the kind of light which incandescent or ]>'. 
phorescent objects emit, or which other bodies reflect, so 
that if a celestial object cannot be otherwise examined, we 

can still find out something about its chemical properties 

by means of the kind of light which it sends us. 

10. If we take bodies which have the same chemical prop- 
erties, and are in the same mechanical condition, — that is, 
bodies which are equally warm, and as much alike as may be 
in every way which our - i j»t that 
they may be of different sizes, — we then find that the larf 

is also the heaviest By this we mean that it requires more 
exertion to lift a large piece of lead, for instance, than a small 
one ; and that when it is lifted it can be made by proper means 
to do more work than the small piece while it is coming back 
to the level from which it was lifted. For example, the wh< 
of a large clock require a large weight to make them turn. 
This gives us a notion that the weight of a body depends on 
the quantity of matter which there is in it ; so that it is sup- 
posed that a piece of lead has more matter in it, or has a 
greater mass, as we say, than an equally large piece of m 
But we should have no reason for believing this if we did not 
know that when we melt some lead and make two bullets of 
different sizes from it. so that neither has any hollow place in 
it, or can be shown to be less compact than the other, the 



Sec. io.] Properties of Matter. 7 

larger is always the heavier ; and that the same general prin- 
ciple applies to wood as well as to lead, and to everything else 
that we know of as well as to lead and wood. It is still easier 
to show that it applies to liquids and gases than that it ap- 
plies to solids, because the particles of liquids and gases can 
move among each other so freely that there is apt to be less 
difference between different parts of a liquid or gas than be- 
tween different parts of a solid. If we cut two pieces of wood 
from the same log, one of them may have a closer grain than 
the other, so that we can see a reason why it should weigh 
more, although it is no larger, than the other piece. But one 
pint of water is almost exactly like another taken from the 
same bucket. We should expect, therefore, to find, as we 
actually do, that if equal measures of a certain liquid or gas 
are weighed under exactly similar circumstances, one is as 
heavy as the other. Hence, when we find that a bottle full 
of quicksilver is very much heavier or harder to move than 
a similar bottle of water, we naturally suppose that the reason 
must be that quicksilver is denser than water ; that is, that 
the particles of the quicksilver are closer together than those 
of the water, so that more of them are contained in the same 
space. However, this supposition is not necessary to enable 
us to study the simpler portions of natural philosophy and 
astronomy. When two material objects are said to be equal 
in mass, what is meant is that it will take as much force to 
give one of them a particular movement as is needed to move 
the other just in the same manner and just as far. If we say 
that one object has more density than another, we mean that 
any portion of the denser object will have more mass than a 
portion equal to it in bulk of the other object, or that equal 
masses of the two objects will differ in bulk. 

11. Every material object has some mass and density ; but 
how dense it is, compared with others of the same bulk, de- 
pends on several circumstances. Such circumstances are, 
first, chemical constitution ; a ball of lead has more mass 
than an equally large iron ball. Secondly, the density of a 
body depends on its compactness ; a loaf of bread is larger 



8 Outlines of Astronomy. [Sec. ii. 

than the flour and water it contains, which would weigh as 
much in any other form as they do in the form of bread. 
Thirdly, density depends on temperature, and, generally 
speaking, decreases as the temperature rises ; a gallon of 
hot water is lighter than a gallon of cold water. Fourthly, 
the state of aggregation of the particles of a body affects its 
density ; that is, when the body is a solid, it has not the same 
density as when it is a liquid, and it has still another density 
when it is a gas. On a wet day in winter, for instance, water 
often exists about us in all three forms, of ice, moisture, and 
invisible vapor ; in all three forms it may have the same 
temperature, so far as the thermometer can show it, and it 
is the same thing chemically in all three forms. M 
we cannot see that the particles of a compact piece of ice, or 
of the vapor in the air, are imt as close together as thost 
the liquid water. Still, the ice is not so dense as the water, 
and is denser than the vapor. It usually happens that a solid 
is denser than the liquid form of the same substance, but 
water is a well-known exception to this rule. 

12. Facts like these have occasioned many notions to 
spring up about the way in which particles of matter 
combined together in material objects, and the way in which 
matter is affected by heat. But a knowledge of the I 
alone is sufficient to enable us to understand the principles 
of astronomy. 

13. What has just been stated about material objects may 
be summed up as follows : — 

All matter has some chemical constitution, mass, and den- 
sity, and may be divided into parts : it may exist in different 
states of aggregation, that is, as solid. Liquid, and gaseous 
matter; it may have more or less heat, and may be a source 
of light, or may only reflect light received from other sour 

14. Matter has other important properties, such as those 
on which depend the facts called electrical and magnetic 
phenomena. These properties have undoubtedly much to 
do with many events which come under the notice of 
astronomers ; but so little is yet known of the nature of 



Sec. 14.] Properties of Matter. 9 

their connection with such events, that it will be enough for 
us merely to notice their existence. 

15. It may be thought that it" matter is whatever our 
senses show us, then light and heat, for example, must 
be matter. This was, in tact, an old opinion, now given up. 
But, strictly speaking, we are informed by our. senses, not 
of light and heat by themselves, but of bright and hot bodies. 
In the same way, we do not see colors by themselves, but 
colored objects. However, color, like many other words, is 
used in a variety of ways, which may easily puzzle people 
who are not good reasoners. The full meaning of such 
words can only be learned by learning all the facts to which 
they relate : and the student who understands this will not 
be likely to become confused by the imperfections of lan- 
guage, the use of which is the only way men have of telling 
others what they have observed. 



to Outlines of Astronomy. [Sec. 16. 

CHAPTER III. 

THE MATERIAL UNIVERSE. 

16. Every material object is a part of the material uni- 
verse, which is often simply called the universe. The differ- 
ence between the universe and matter in its widest sense is 
that, in speaking of the universe, we think of the separate 
shapes and properties of the objects of which it is COmpoa 
but take no notice of these shapes and properties when we 
speak of matter. The extent of the universe is entirely un- 
known ; but, as far as we are concerned with it, it is limited 
by the capacity of our senses. That is, the universe which 
we are to attend to in studying astronomy comprises every 
material object of which men know any thing, and no Oth< 

17. There are many questions about the universe with 
which people sometimes amuse and sometimes perplex them- 
selves, but which are not properly part of any science at all. 
There are others which are logical or mathematical, but not 
strictly astronomical questions. Still others are really]' 

of astronomy, but require so much knowledge of mathem.r 
and logic that very few astronomers are capable of Stud) 
them ; and other people, of course, cannot form any rational 
opinion upon them at all, or learn what is thought about 
them by those who can study them. It is curious that these 
questions, which can be comprehended only by a few unusu- 
ally learned men, and which even those who can comprehend 
them cannot answer, are often supposed to be so simple that 
anybody may set himself to making guesses about them, and 
writing down his guesses with the notion that he is making 
discoveries in astronomy. Inquiries into the past history of 
the universe are often made by mere guess-work of this kind. 
It is natural that people should ask how the universe came 
to be what it now is ; and the question may some day be 



Sec. 17.] The Material Universe. ii 

partly answered. But at present no distinct answer can 
be given ; .\nd even to understand the reasons which have 

led some distinguished astronomers to form opinions upon 
this subject, is out of the power of any one who has not thor- 
oughly studied what is called theoretical astronomy. The 
less people can know, however, the more they seem disposed 
to conjecture : and one opinion or another about the origin 
of the universe, or some part of it, is maintained by many 
who have not the means of forming any sensible judgments 
at all upon such a question. In considering the history of 
astronomy, we shall have occasion to notice such opinions 
as deserve respect with regard to the condition of the uni- 
verse before it assumed that structure which observation lias 
shown it to have ; but nothing is as yet generally admitted 
by competent judges to be known of this early condition. 

There are interesting questions relating to the space 
which contains the universe ; but they are too difficult for 
study, except by well-trained minds, and are not strictly astro- 
nomical, but rather geometrical questions. We occasionally 
see them dismissed in a weak and unscientific way, which 
leads to no useful result. Of this kind are such questions as 
the possibility that the number of the stars is infinite in the 
strict sense of that word. In studying astronomy, as has 
been said, we must confine our attention to what can be actu- 
ally observed. 

19. One very common inquiry deserves some notice in a 

book of this kind, although it is one of that class of questions 

which have been described as not belonging to any science. 

Its object is to decide whether other parts of the universe 

than the Earth are inhabited ; and whole books have been 

written upon this subject. It is a good subject to write about, 

use, as it is commonly handled, it has hardly any tiling 

lo with facts, and a great deal with the sense in which 

people piease to take certain words ; and for the same reason 

red any part of science. Nobody can say 

exactly how much like a man a creature living elsewhere than 

on the Earth must be before it is tit to be called an inhabi- 



12 Outlines of Astronomy. [Sec. 19. 

tant of whatever place it occupies. To make the question 
plainer, suppose we alter it, and ask only whether a man 
could continue alive if he were suddenly removed from the 
Earth and set down somewhere else. It is not at all likely 
that he could, because we know that men are easily killed by 
what seem comparatively slight changes in the condition of 
things about them. Exposure to a climate to which they are 
unaccustomed, for instance, is enough to kill many peo] 
and a climate which belonged to a place entirely removed 
from the Earth would not be apt to be as much like 
trial climates as they are like each other. However, most of 
what has been written on this subject, so far as it has any 
distinct object, seems to aim at deciding whether anv thing 
is known about the parts of the universe beyond the Earth 
which will enable us to judge whether we could live in any 
of them. So far as we can tell, the prospect is rather dis- 
couraging to any person who should wish to emigrate from 
the Earth with his present body, and should find means of 
doing so. We can see that there are some differences be- 
tween the Earth and other places, and we defnot know how 
many other differences there may be which we cannot - 
But whatever we find out, we can always imagine something 
not yet found out, which would make it either possible or 
impossible, whichever we wish to believe, for us to live in 
anyplace we have not yet visited. Astronomical dis< 
then, will do very little to put an end to such a dispute. 

20. Let us try one other way of putting the question. Are 
there any rational animals living in the universe except those 
upon the Earth ? If astronomers could see any such aniir 
and find out the nature of their minds by their actions, the 
question could be treated as a matter of fact. The Moon is 
the nearest place in which such animals can be looked * 
and an animal would have to be two or three thousand feet 
round before we could see it on the Moon plainly enough to 
tell what it was with any instruments we have at present. We 
are not likely, then, to make discoveries of this kind for some 
time to come. Meanwhile, some people argue as if animals 



Sec. 20.] The Material Universe. 13 

must grow in every place that is at all like the Earth, and 
others argue as If there could be none in any place at all 
unlike the Earth. Arguments of both these kinds are of no 

value in helping us to knowledge. It" we knew just what there 
was about the Earth that made it a suitable place lor animal 
life, then we could inquire whether such circumstances ex- 
isted elsewhere. But we do not yet know why the Earth is 
the dwelling-place of man and other creatures; we only know 
that it is. We cannot say, then, that places like the Earth in 
many ways are ht for animals to live in ; nor can we say that 
places unlike the Earth are unfit to support animals made to 
live in such places. If a fish could think at all upon the 
question, he would think, perhaps, that nobody could live 
out of the water. It is just as foolish for us to say that a 
rational animal could not be so made as to live in water or 
in fire. We see, then, that the question we have just been 
considering is not a scientific question at all ; that is, it re- 
lates to a subject into which we have no means at present of 
inquiring in a rational manner. Knowledge is acquired only 
by studying such subjects as can be systematically investi- 
gated by the help of knowledge which we have already ; it is 
not to be had by making guesses about any thing that comes 
into our heads. We need not blame people for making such 
guesses ; but we are not to suppose that they are studying 
science when they are spending their time in that way. 

21. We will now see what has actually been learned about 
the universe. The principal fact which we shall have to notice 
is that the more men study it, the greater is the variety of the 
objects they find in it. At first sight, all there seems to be in 
the universe besides the Earth is a number of bright specks 
in the sky, most of which are called stars; while two of them, 
led the Sun and Moon, are much larger than the rest, but 
seem to be small compared with the Earth. The stars seem 
much like each other before they have been studied carefully, 
and the Moon seems more like the Sun than like the Earth. 
But men know now that these appearances differ very much 
from the reality. There are many celestial objects which 



14 Outlines of Astronomy. [Sec. 21. 

cannot be seen even with telescopes, and indeed such objects 
are doubtless far more numerous than those which can be 
$een. The Moon is really one of the smallest celestial objects 
which are ordinarily seen, but yet its thickness is one-fourth 
as great as the Earth's. As for the Sun, one hundred and 
eight globes, each equal to the Earth, might be set side by 
side in a straight line within it. If the Earth could be set in 
the middle of the Sun, the Moon would be little more than 
half-way from the middle to the outside of the Sun, if it were 
placed as near the Earth as it actually is. How the Sun com- 
pares in size with the largest celestial objects which can be 
seen is not known exactly, for we do not yet know which of 
the stars is the largest ; but there is reason to think that 
many of the stars are much larger than the Sun. But the 
stars differ much from each other in size and in Other P 
Some of those which seem among the brightest are compara- 
tively small, and resemble the Earth more than they resemble 
the Sun. These belong to the class of celestial objects called 
planets. Most of the stars which can be seen with the naked 
eye, however, are like the Sun in most respects, BO tar as is 
known. Very little, indeed, is known of the stars which 
resemble the Sun, for the nearest of them are at a \ 
distance from us. The thickness of the Sun has just been 
stated as one hundred and eight times that of the Earth : the 
distance between the Earth and the Sun is about one hundred 
and eight times the thickness of the Sun. Now the Deal 
stars which resemble the Sun are more than two hundred 
thousand times as far away from us as the Sun is. When 
we are aware of this, it is surprising that we have any knowl- 
edge at all of such remote objects. 

22. From what has been learned about the celestial objects, 
it seems likely that if we could travel about the universe and 
examine the regions through which we passed as closely as 
we can the ground over which we travel on the Earth, the 
various objects which would come under our notice would be 
somewhat as follows. We should find the ether everywhere, 
not only between the Earth and other objects, but in them ; 



Sec. 22.] The Material Universe. 15 

for this ether is supposed to be so very thin a gas, if it can 
be called a gas at all, as to penetrate all bodies as water 
penetrates a sponge. Our supposed journey would often 
take us through places where there was nothing but ether, 
and we might then perhaps get some more distinct knowl- 
edge with regard to its existence, and, if it exists, with regard 
to its nature, than we can obtain now. However, we may 
take it for granted, until more is known upon the subject, 
that we should rind ether throughout the universe. If it 
has so little density that it can penetrate the densest solids, 
we can easily believe that it scarcely at all hinders the move- 
ment through it of the lightest celestial objects. 

23. We should find moving about in the ether material 
objects of all kinds of chemical composition, of all kinds of 
density, and of all sizes which we can well imagine. Some 
would be solid, some liquid, and some gaseous ; some, prob- 
ably, much colder than any terrestrial object ever is, and 
some, certainly, very much hotter than the hottest terrestrial 
fires. Here and there we should find great spaces filled with 
luminous gases, either incandescent or perhaps only phos- 
phorescent. Such masses of gas are sometimes called clouds, 
but we must remember that they are unlike terrestrial clouds 
in many ways, and especially by being composed of gas, and 
not of liquid or solid particles. We should also find clouds, 
if we like to call them so, partly gaseous and partly liquid and 
solid. Some of these various kinds of clouds would have a 
round shape, like that of the Earth ; but many others of them, 
like terrestrial clouds, would have very irregular forms, and 
might be more or less divided into parts, so that it would be 
difficult to say whether we ought to count these parts as sep- 
arate clouds or not. It is not certain that all these clouds 
would give out light ; there may be among them many which 
cannot be seen from the Earth, because they do not shine, 
and are not near enough to any luminous object to become 
le by the li^ht they reflect to us. 

21. Besides these clouds, or masses of matter not closely 
compacted together, there are other masses which, whether 



16 Outlines of Astronomy. [Sec. 24. 

solid, liquid, or gaseous, are at all events more compact 
than those we have called clouds, and also much brighter. 
The Sun is one of these ; and we may call them all suns. 
Perhaps there are bodies even larger than our Sun, which 
yet give out no light of their own. We should not call such 
bodies suns ; and if they were compact and not cloud-like, 
we should regard them, even if they had no solid matter 
about them, as planets ; or, in other words, as belonging to 
the same class of objects with the Earth. So far as is 
known, all these large and compact material objects, whether 
they are suns or not, are globular in shape, like the Earth ; 
and it is reasonable to suppose that they all have the tl 
principal kinds of movement which the Earth has : that is, 
that they are all falling, advancing, and rolling. When sev- 
eral of them are much less distant from each other than from 
other similar objects, they form what is called a system. The 
Sun, the Earth, and a number of other bodies, form a system 
known as the Solar System, because the Sun is the most 
important of the bodies which belong to it. But although 
the large bodies which compos< m are not so far from 

each other as from other systems, their distance from each 
other is great compared with their size ; and so is usually the 
distance between any two systems, compared with the extent 
of either system. For instance, as we have seen already, it 
would take over a hundred bodies as Large as the Sun to 
reach from the Sun to the Earth ; and the distance of our 
system from the nearest system known to us is over two 
hundred thousand times as great as that separating the Earth 
and Sun. The objects we have called clouds often extend 
over more space than would suffice for many systems like 
the Solar System. Several systems may of course all form 
parts of one larger system. 

25* All these large bodies, whether clouds, suns, or plan- 
ets, seem to occupy a very small part of the space in the 
universe ; and no doubt the spaces between them are seldom 
entirely vacant, or filled only by the ether. There is reason 
to think that, just as among terrestrial objects we find the 



Sec. 25.] The Material Universe. 17 

smallest the most numerous, so, too, celestial objects are 
scarce in proportion to their size. There are small gaseous 
clouds as well as large ones, and possibly many as small as 
terrestrial clouds, or smaller. There are certainly millions 
oi little solid bodies moving about in our own part of the 
universe ; and probably some of them are mere grains of 
dust. These little bodies are often of irregular form, like the 
stones and dust of the Earth ; and they are so plenty that if 
we had not the air to keep them off they would make the 
Earth a very unsafe place for us. As it is, they sometimes 
force their way through the" air and fall to the ground, 
although the air is a much more effective defence against 
these aerolites, as they are called, than would at first be sup- 
posed. Little objects of this kind often move in large swarms 
or clouds. 

20. If, then, we could travel through the universe accord- 
ing to the supposition just made, we should very frequently 
meet little particles of matter in one form or another, and 
often come across moderately large material objects, or col- 
lections of small bodies ; but we should find great bodies like 
the Earth only occasionally, even if our rate of travel was 
thousands of times faster than that of our locomotive engines ; 
and bodies like the Sun would be very seldom encountered. 
But in looking at the sky from the Earth, these suns are 
almost all that we see ; and it is only by noticing every thing 
we can, and attending carefully to the meaning of our obser- 
vations, that we can show the smaller and darker objects in 
the universe to be as numerous as they are now considered 
to be. 

we cannot separate the material objects in 

the universe into entirely distinct classes, because, however 

make the divisions, we always find objects partaking more 

or less of the character of two or three of the classes we have 

formed. Still, for the sake of convenience in studying and 

e universe, it is customary to cl issify the ol j 
it contains, and we will accordingly consider them in s< 
rate classes. But we must remember that these classes arc 

2 



18 Outlines of Astronomy. [Sec. 27. 

artificial groups, which depend for their formation upon what 
we have learned up to any particular time rather than on the 
arrangements of nature. It must not surprise us, then, to 
find that as new objects are discovered, it often appears that 
they belong as much to one as to another of the classes which 
previous astronomers have formed ; and from time to time it 
becomes necessary to change our classification so as to adapt 
it better to the new state of our knowledge. 

28. At the present time the celestial objects are usually 
divided into five principal classes, which are the following : — 

a. Suns, or fixed stars. Tiiese are large, globular, incan- 
descent, and compact, though probably not solid, bo<. 
The name of fixed stars was originally given to all bodies of 
this class except the Sun, because, as seen from the Earth, 
they did not seem to change their positions with respect to 
each other from year to year. But this was merely because 
they are so far from us. 

b. Planets. This name means wanderers, and was or 
nally given to certain bright stars which were seen gradually 
to change their positions with regard to each other and to 
the fixed stars. But at the present time any body would be 
called a planet which gave out little or no light of its own, 
but was large enough, and always near enough to some sun, 
to shine by the light it reflected. No planets are known to 
exist except those which are seen by the light of our own 
Sun; but there is reason to think that other suns also have 
planets not too far from them to be regarded as belonging to 
the systems of which those suns are the chief members. 

c. Nebulae. This name means clouds, and is applied to 
the enormously large clouds, shining by light of their own, 
which have already been mentioned. 

d. Comets. This name is derived from the Greek word for 
hair, and was originally applied to certain celestial objects 
which are occasionally seen for a time with streamers of light 
called tails attached to them. But now, any thing which 
looks like a nebula, but is near enough to us to have its 
apparent position among the other celestial objects continu- 



Sec. 28.] The Material Universe. 19 

allv changed by its motion, is called a comet. We know of 
no comets except those which occasionally approach our Sun 
and retire from it again. 

c. Meteors. This name only means objects which arc 
aloft or on high : it was not originally applied to any celestial 
objects except such as were seen only for a short time at 
once. But it has been applied to all remarkable appearances 
in the sky, such as comets and northern lights, as well as 
shooting stars. However, modern writers in English gen- 
erally apply the name only to those comparatively small 
celestial objects which appear as shooting stars when they 
enter the Earth's atmosphere. Meteors, then, are any 
celestial objects too small to be conveniently classed as 
suns, planets, nebula?, or comets. 

29. It will be seen from this account of astronomical clas- 
sification that it may be doubtful, as our knowledge of any 
celestial body increases, whether it is most properly to be 
called, for example, a sun or a planet, a planet or a meteor ; 
in fact, we know of many planets so small that there is little 
to distinguish them from meteors. However, as all of them 
that are known are situated in one particular region of the 
Solar System, they are sometimes spoken of as forming a 
class by themselves, and are called asteroids ; but they are 
commonly called planets, for reasons which will appear when 
they are more fully described. 

30. Certain planets of a particular kind are called moons 
or satellites ; but they need not be specially described at 
present. 



2o Outlines of Astronomy. [Sec. 31 



CHAPTER IV. 

SUNS, OR FIXED STARS. 

31. In describing the first of the classes of celestial objects 
named above, we will begin with our own Sun, since we have 
much more knowledge of it than of any other. But we shall 
see that this knowledge is, after all, very imperfect. It is not 
yet certainly known whether the Sun is solid, liquid, or gase- 
ous ; but the prevalent opinion at present seems to be that 
it is a great globe of gas, although th >f its interior 

must be compressed and condensed to an extent which must 
make them very unlike any terrestrial gas with which we are 
acquainted. The exterior parts of the Sun are certainly g 
eous. In other words, it has an atmosphere, as the Earth 
has : but the Sun's atmosphere is by far the larger of the I 
even when viewed with regard to the bulk of the body it en- 
closes ; that is, the depth of this atmosphere is equal : 
much greater fraction of the thickness of the Sun than the 
fraction of the Earth's thickness which is probably equal to 
the depth of the air. Another difference between the atmos- 
pheres of the Sun and the Earth is that all that part of the 
Sun's atmosphere of which we know any thing is a source 
of light, or shines by light of its own, like the Sun itself. 
But if this atmosphere were nearly as bright as the body-of 
the Sun, then it would look like part of the Sun, while, in 
fact, its light is so faint compared with the Sun's that it can 
only be seen by instruments made purposely to examine it, 
except at times when the Moon comes between us and the Sun, 
and causes vthat is called a total solar eclipse. Then a great 
deal of the luminous atmosphere of the Sun can be seen 
without the help of instruments ; but at the same time some 
reflected light is seen in the sky, which cannot well be dis- 
tinguished from the light of the Sun's atmosphere, so that on 



Sec. ji.] Suns, or Fixed Stars. 21 

such occasions the exact limits ot this atmosphere cannot be 
1. Although the Sun's atmosphere is a source oi Light, 
Sun would be brighter without it, for it cuts off more 
light coming from the Sun than it sends out itself. Near 
the surface oi the Sun. however, it is so bright that it may 
actually increase the Sun's apparent magnitude. 

3*2. It is not known whether the interior of the Sun, if we 
could see it, would be as bright as that part of it which we 
actually see. and call its surface. The matter presenting to 
us this surface, and lying within it, but comparatively near 
it. forms what is called the photosphere of the Sun. Most 
observers think that if it is solid or liquid matter, it is in the 
form of clouds ; that is. it must consist of multitudes of little 
solid or liquid particles floating in gases of some sort, as our 
clouds tioat in the air. But the photosphere maybe itself 
ous ; and in that case it is composed of much heavier and 
more compact gases than those which constitute the atmos- 
phere which has been mentioned. Another theory is that 
the photosphere, or part of it, is a liquid ocean covering the 
Sun. Whether solid, liquid, or gaseous, the photosphere is 
incandescent, as is obvious enough to other people than 
astronomers. The actual amount of light and heat which 
it sends out is too great, and our means of measuring it are 
imperfect, to admit as yet of very accurate knowledge 
upon this subject. Still, some measurements have been 
made of the light and heat of the photosphere ; and the 
difference between the heat of the iron which it probably 
contains, and what we call white-hot iron, is no doubt many 
DOmers think many hundred) times greater than 
the difference between our white-hot iron and cold iron. 
The light of the photosphere, too, is far more intense than 

terrestrial light. Matter so intensely incandescenl 
that which makes up the photosphere cannot form the ordi- 
nary chemical combinations which occur among terrestrial 
SUbst many, at least, of these combinations are found 

xperiment to be broken up by of heat which 1 an 

be produced artificially. When the simple kinds of matter or 



22 Outlines of Astronomy. [Sec. 32. 

elements which make up a compound body have been sepa- 
rated from one another by heat, they are said to be disso- 
ciated ; and this state of dissociation is thought to be the 
ordinary condition of the matter of the photosphere and that 
part of the Sun's atmosphere which lies close to the photo- 
sphere. But it has been shown, by a method hereafter to be 
explained, that many chemical elements which are found on 
the Earth also exist as gases in that part of the Suns atmos- 
phere immediately surrounding the photosphere, where many 
other elements, of which we as yet know nothing, are also 
known to exist. The chemical nature of the photosphere 
itself cannot be observed with our present means. Probably, 
however, the photosphere, like the atmosphere about it, con- 
tains most if not all simple kinds of matter which appear upon 
the Earth, and others also, but not combined chemically as 
we find them he»*e. 

89. The Sun has undoubtedly all the three principal kinds 
of movement which have been said to belong to the Earth, 
and probably to all celestial bodies. But its rolling » 
ment is the only important movement it has which we are 
as yet able to learn much about ; and for the present we will 
consider this alone. In order to do so, we must fust It 
distinctly what a rolling movement is. Strictly speaking, the 
movement we are to describe is rotation, and not rolling ; for 
we commonly say that a ball rolls only when it turns round 
and moves forward at the same time. So, too, the wheels 
of a locomotive steam-engine may be said to roll upon the 
track ; but the wheels of a stationarv engine in a factory are 
not said to roll, but to revolve or rotate. Now the Earth and 
the Sun are properly enough said to roll, when we consider 
their various movements in connection with each other; but 
when we confine our attention to the difference between the 
movement of one part of either body and its other parts, it is 
customary to give the movement of the whole body the name 
of rotation. No part of a body, the whole of which is 
moving, can be absolutely at rest; but the peculiarity of 
rotation is, that by supposing any body which has only that 



Sec. 35.] Suns, or Fixed Stars. 23 

movement to be divided into small enough parts, we can find 
parts oi it which move in a given time through a distance 
;ller than any which we please to name. For instance, the 
main shaft of a steamboat, although it moves along with the rest 
of the vessel, has only a movement oi rotation when the motion 
of the vessel is left out of consideration. If, now, we consider 
the movements of the different particles of iron in the shaft, 
we see that some near the outside of it move farther in the 
same time than others not so near the outside. We see, too, 
that there must be some of these inner particles which move 
less than the millionth of an inch during one revolution 
of the shaft, and some which move less in the same time 
than any other very small distance we may name, provided 
that these particles are supposed to be sufficiently small. 
But however small we suppose them, the parts of each 
particle move at different rates ; and so we may go on 
dividing them as long as we please, without finding one or 
any part of one which does not move at all. To make it 
easier to describe and study this movement of rotation, we 
suppose a straight line, without any thickness at all, drawn 
through the interior of the shaft, but not forming any part 
of it. This line must be so drawn that the particles of the 
shaft move less the nearer they are to this line ; so that the 
line lies among those particles which move least, and may be 
considered as having no movement of its own. Such a line 
in any object which has a movement of rotation is called the 
axis of the object, or the axis of rotation of the object. An 

- of rotation, then, is no part of the object which turns 
alxmt it, but has a particular position in that object, without 
taking up any space there. It is, in fact, what every straight 
line is considered in geometry, — something having length and 
position, but not occupying space. 

Mi An axis of rotation does not always pass through the 
middle of the object to which it belongs. There are pie 
of machinery, for instance, called eccentrics, because they 
turn about axes which lie out of their centres. Bill when an 

- of rotation is not fixed mechanically, as are the azefl of 



24 Outlines of Astronomy. [Sec. 34. 

pieces of machinery, but is free, like the axis of a bullet 
discharged from a rifle, or like that of any ball rotating in 
the air or the ether, then it must pass through the middle of 
the object which turns about it, unless the matter of which 
that object consists differs in density in different parts of the 
object. In every case of this kind the axis passes through 
what is called the centre of gravity of the object. This 
centre of gravity occupies such a place in any object of 
regular shape, that there is as much of the mass of the 
object in any direction from it as in the opposite direction. 
In most of the celestial objects of which we know any tbi 
the matter composing them is distributed evenly enough to 
make their axes pass through their middle points, so far as 
can be perceived. 

35. But an axis may not always keep the same place in the 
object to which it belongs, even if it always passes through 
the middle of that object. When a ball rolls along the ground, 
its axis of rotation usually changes very frequently; that is, 
those parts of the outside of the ball which are turning slow- 
est or quickest will not continue the same for any length of 
time. This is generally due to the roughnesses of the ground. 
When no other body disturbs the movement of a rotating 
body, its axis usually keeps its place. The Earth's axis, tor 
instance, keeps its place perfectly, so far as can 1 
at present. There may be a little doubt whether the a 
of the Sun is equally stationary, because different ol 
have not precisely agreed about its position ; but it is likely 
that this is wholly due to our imperfect means of determining 
what that position is. However, the axis of a fluid or gaseous 
globe like the Sun, constantly agitated by irregular move- 
ments within it and in its atmosphere, may not be as steady 
as that of a comparatively solid and quiet body like the Earth. 
But if the place of the Sun's axis varies at all, the variation 
is slight, and we may accordingly consider the Sun as turn- 
ing about a fixed axis passing through the exact middle of the 
globe enclosed in the photosphere. The poles of the Sun, 
like those of the Earth, are the points of its axis which lie in 



Sec. 35.] Suns, or Fixed Stars. 25 

its surface. Hence the nearer any part of the photosphere is 
to one of the poles of the Sun the smaller is the distance over 
which the Sun's rotation carries it in a given time ; and the 
parts o\ the photosphere which are carried farthest by this 
rotation are those which lie about as far from one pole as 
from the other. 

3tf. We now need names by which the poles of the Sun 
may be distinguished from each other. The Earth's poles 
are known one as the north and the other as the south pole; 
but if we are asked to explain the meaning of the words north 
and south, we can only say that the north pole of the Earth 
is the pole nearest some particular country, Greenland, for 
example, and that north means towards the north pole. But 
there are no fixed marks on the surface of the Sun, such as 
the continents and islands on the surface of the Earth. What 
marks there are do not last long at a time, as we shall see 
hereafter, and therefore are of no service in distinguishing 
between the poles of the Sun. 

37. Again, the Sun's axis is not always in the same posi- 
tion with respect to that of the Earth. Sometimes one pole 
of the Sun and sometimes the other is the nearer to the Earth 
of the two. Hence we cannot distinguish between them, as 
we might do otherwise, by means of their comparative near- 
ness to us. We must therefore make use of the following 
method. 

38. Although no man, or at least no civilized man, has 
ever come very near either pole of the Earth, yet the study 
of astronomy has taught us in what part of the sky the various 
stars would be seen by an observer stationed anywhere upon 
the Earth or the Sun, and consequently at any one of their 

For instance, we know that any traveller who reaches 

the nor*' the Earth, at any time within a few centuries 

1 now. will have the star Polaris, known also as tin- North 

irly in his zenith. This means that it will be over 
his head, nearly as far as possible from the horizon. We 
kno iiat other stars he could see, in clear weather, 

while the Sun was below his horizon. Mo.st of the.^e stars 



26 Outlines of Astronomy. [Sec. 38. 

would remain the same from year to year. They would seem 
to change their places continually with respect to the terres- 
trial objects which might be in view, but they would not rise 
or set. At the south pole of the Earth, an observer would 
continually have in view another set of stars, scarcely any 
which would be visible from the north pole ; and he would 
scarcely ever see any of the others. The star Polaris would 
of course be beneath his feet, on the other side of the Earth. 

39- Now if we could get a view of the stars from either of 
the poles of the Sun, we should likewise see constantly a | 
ticular set of stars. From one of the Sun's poles the star 
Polaris would appear to be about one quarter of the way from 
the zenith to the horizon ; and although we should see some 
of the stars visible from the south pole of the Earth, and 
should not see some of those visible from its north pole, vet 
the greater number of the stars in sight would belong to the 
set seen from the Earth's north pole. At the other poll 
the Sun we should not see Polaris, and most of the visible 
stars would belong to the set seen from the Earth's south 
pole. We may accordingly call that pole of the Sun from 
which Polaris could be seen the Sun's north pole, and the 
other its south pole ; but in doing so, we must remember that 
we are using the words north and south in a somewhat dif- 
ferent sense from that in which they are applied to terrestrial 
objects. When the region around the north pole of the Sun 
is in sight from the Earth, it is of course in that part of the 
Sun toward the northern sky. 

40. The word equator is used with respect to the Sun 
much as it is with respect to the Earth. That is, the Sun's 
equator is the boundary line which we may suppose drawn 
between those parts of its surface nearer to its north than to 
its south pole, and those nearer to its south pole than to its 
north. An equator, like an axis, takes up no room, and is no 
part of the object to which it belongs. ]\ we suppose the 
Sun divided into halves by its equator, the half which con- 
tains the north pole is called the northern hemisphere of the 
Sun, and the other its southern hemisphere. 






Sec. 41.] Suns, or Fixed Stars. 27 

41* Even if there were no stars in the sky, wc could still 
distinguish between the north and the south pole of the Sun 
by methods of astronomy like those which show us what 
stars would be visible from places never visited by man. But 
if there were no stars to assist astronomers in their observa- 
tions of the Sun, it is likely that the science of astronomy 
would now be so little developed that scarcely any thing 
would be known of the Sun's movements. 

42. The rotation of the Sun is of the kind called direct 
rotation ; an object turning the other way would have retro- 
grade rotation. To make it clear what this means, let us 
suppose two wagons, one moving eastwards and the other 
•wards. The wheels of the first wagon will have direct, 
and those of the second retrograde, rotation. If we stand on 
the north side of the road, facing the wagons, the tops of the 
wheels of the eastward bound wagon will turn from right to 
left, and those of the other wagon's wheels from left to right; 
seen from the south side, the motions will be reversed. Now, 
if an observer could be placed outside of the Sun, near its 
north pole, so as to look towards the Sun along the line of its 
axis, then the side of the Sun which would appear to him to 
be uppermost would be turning from right to left, and accord- 
ingly we say that the Sun's rotation is direct. The terms 
direct and retrograde, then, as applied to the movements of 
celestial objects, depend for their meaning on the use of the 
words north and south. The movement of one object round 
another may be direct or retrograde as well as the rotation 
of a single object. In fact, if we consider the separate parts 
of any object which rotates, we see that some of them move 
round others. But every direct or retrograde movement 
must take place around some line which we can consider as 
running north and south. If we know of no such line, the 
terms direct and retrograde lose the meaning which they 
have in astronomy. Hence a figure drawn on paper will not 
be of mu' ' nee in understanding them. 

!'.{. The time which the Sun requires for one complete 
rotation is about 25J of our days. At first sight, this state- 



28 Outlines of Astronomy. [Sec. 43. 

ment seems to need less explanation than that just made 
about the way which the Sun turns. In fact, however, it is 
hard to get a really distinct notion of what a complete r< 
tion is. When a wheel rolls along a track, WC say that it has 
turned round once in the time which has been ne< 
every part of its rim to come once into contact with the 
track ; and this notion is clear enough. But in formil 
consider the track as station. iry. When we remember that 
the track itself is turning along with the rest of the Earth, we 
see that there is a sense in which the wheel has not tin 
round exactly once in the time during which every part of its 
rim has once touched the track. In counting the rotations 

of any thing, then, we need something to reckon from, whit h 
we can consider fixed and motionless. But we know that the 

celestial objects are all in motion. If we assumed that the 
Earth Had no motion except that of rotation, we should h 
to say that one rotation of the Sun Occupied about 27 days 
instead of 25$. This difficulty cannot he entirely rem* 

except by acquaintance with practical astronomy; hut the 
principle according to which the rotations of any celestial 

object must he counted may perhaps he partially explained 
by examples of its application to terrestrial movements. 

I 1^ Suppose a model to be made of a Hock of birds in 
flight, showing the exact places of all the birds in the flock at 
some particular moment with respect to each other j and sup- 
pose another model to be made, showing in the same manner 
the places of these birds with respect to each oth 
seconds later. We could then, by comparing the m<> 
examine the changes which had taken place during th<>M- few- 
seconds in the arrangement of the birds. To get 1 I 

definite notion of this comparison, let us suppose that 

calculate separately for each model what would be called the 
centre of gravity (34) of the Hock in the arrangement which 
that model represented, and put into each model a little mark 
of some kind, such as a small shot, to show whereabouts this 
centre of gravity is. We could then consider how any bird 
in either model was placed with regard to a line drawn from 






Sec. 44.] Suns, or Fixed Stars. 29 

that bird to the centre of gravity of the flock. To be accu- 
rate, we should have to draw the line from the same part of 
the bird in the two models. In one model, the bird might be 
facing towards the centre of gravity, and in the other facing 
away from it. We might then consider, if we pleased, that 
he had turned half round, or made half a rotation, while the 
birds were passing from one to the other of the arrangements 
represented by the two models ; and if, instead of two models 
only, we could have one for any instant that we could name, 
we could then trace the gradual progress of the bird's rota- 
tion. 

45, If the movements of celestial objects were apparently 
as irregular as those of a Mock of birds, there would be little 
satisfaction in investigating them in any manner like that 
described in the preceding illustration, which is, of course, 
not intended to exhibit the actual method by which the Sun's 
period of rotation is determined. But it is a general prin- 
ciple that, when we have nothing that can be considered 
motionless from which to measure the movements of other 
objects, we must supply the want by using the positions of 
those objects with respect to each other at a given time as a 
fixed model, so to speak, with which their positions at other 
times may be compared. This principle is that on which we 
supposed ourselves to proceed in examining the movements 
of birds ; and it is that on which astronomers must proceed 
in examining the movements of celestial objects. The laws 
which regulate the course of many of these objects are so 
well known that their effect can be calculated for any moment 
within many centuries, past and future. We might actually 
construct a model showing the directions of all these ol i 

ome among them at any such moment ; but, 
in practice, the resu!* :< illation are sufficient for 

pur. :d no actual model is needed. Thus \\c can 

determine the appearance of the St oly from 

places we have never reached, but also at times before astron- 
omy was studied. 

46. It appears, from what has been said, that as we learn 



30 Outlines of Astronomy. [Sec. 46. 

more about astronomy we constantly have to correct our 
former conclusions about the movements of certain objects 
by means of the new knowledge which we acquire with regard 
to the relations of these objects with others. Thus, if we 
learn more hereafter than we now know about the Sun's 
movement among the other stars, we shall have to alter the 
figures which now express its period of rotation. But this 
alteration will be very slight indeed ; and before it can be 
perceptible at all, we must have learned to observe the Sun 
and to determine its period of rotation with regard to the 
Earth much more accurately than we can at present. 

47. The comparative thickness of the Earth and Sun has 
already been stated (21). From this it appears by geunv 
that the bulk of the Sun is over one million and a quarter 
times that of the Earth. The Sun, however, has been found 
not to exceed the Earth in mass as much as in bulk. Still, 
as the Sun would outweigh three hundred and twenty thou- 
sand bodies each as heavy as the Earth, its actual mass is as 
much beyond our distinct comprehension as if it were heavy 
in proportion to its bulk. The small comparative density of 
the Sun is obviously one of the reasons for supposing it to 
be a gaseous, or at least not a solid, body. 

48. In speaking of the bulk of the Sun, we take into ac- 
count only the globe lying within the outer limits of the pho- 
tosphere, since this is all which can be readily seen. But 
our knowledge of the Sun's mass is derived from our obfl 
vation of the influence it exerts upon the movements of other 
bodies, and this mass is accordingly that of the Sun and its 
atmosphere taken together. The mass of this atmosphi 
however, must apparently form only an insignificant part of 
what we call the mass of the Sun. 

49. Although it has long been known that the Sun is a 
globe, this fact is not immediately evident to any one who 
sees the Sun, but was originally learned only by putting 
together the results of many observations of other obj< 

as well as of the Sun itself. It seems, when we look at it, 
like a round flat object, one side of which is turned towards 



Sec. 49.] Suns, or Fixed Stars. 31 

us. In fact, however, the various movements of the Earth 
and Sun are constantly changing our view of it, so that all 
the outer portions ot the photosphere are brought in sight 
of the Earth at one time or another. The disk of the Sun is 
the name given to that part of the photosphere which we can 
at any one time ; so that in speaking of the disk we are 
speaking of the Sun as it appears and not as it is. The edge 
of the disk is called the limb of the Sun. That part of the 
limb which rises and sets first is called the preceding limb, 
and that which rises and sets last is called the following 
limb. The words preceding and following are much more 
convenient than western and eastern for use in astronomy, 
because it is sometimes hard to tell what is meant by west 
and east. The northern limb of the Sun is of course that 
part of its limb between its preceding and following limbs on 
that side of the disk which is nearest the northern sky ; and 
the southern limb is opposite to the northern. We need not 
lav down any exact boundaries between these different limbs ; 
when we have to speak precisely, we use other terms. To a 
terrestrial observer stationed north of the Tropic of Cancer 
the northern limb of the Sun always seems uppermost at 
noon. 

50. The Sun's disk is too bright to allow us ordinarily to 
look directly at it ; and when it is studied with telescopes, it 
is necessary to take care to protect the eyes properly against 
the light and heat which would otherwise seriously injure 
them. The safest way of doing this is to form an image of the 
Sun by means of a telescope upon a screen, and not to look 
through the telescope at all. When the disk is closely ex- 
amined In this or any other suitable way, it is usually found 
not to be equally bright in all parts, although the darkest 
parts of it are undoubtedly very bright, and only appear 
dark by contrast with the brighter parts. 

51. In the first place, the disk is on the whole brightest 
in the middle, and gradually grows darker towards the limb. 
On this account, a good photograph of the Sun generally 
makes it look somewhat solid, or like a globe, BUch as it 



32 Outlines of Astronomy. [Sec. 51. 

really is, instead of making it seem like a mere flat disk. 
This, however, is only an effect of light and shade, and the 
photograph of a round piece of pasteboard properly shaded 
would have the same solid appearance. In order to under- 
stand why the Sun's disk is brightest in the middle, let us 
first consider why the whole Sun usually seems brighter the 
higher it seems to be in the sky. When the Sun has just 
risen or is about to set, we look at it along the ground, so 
that between us and it there is a great deal of that del 
and heavier part of the air which lies close to the Earth. 
But when we look at the Sun in the middle of the day, we 
are looking almost directly away trom the Earth, so that 
the Sun's light reaches us after traversing only so much of 
the air as lies nearly above the place from which we look. 
The air grows thinner very fast as we go farther from the 
Earth, so that wherever its limits are, the great mass of it, 
at all events, lies within a few miles of the land and 
Hence it appears that the higher the Sun stands in the sky 
the smaller is the mass of air between us and it. The air is 
not so transparent as we are apt to think it, so that a great 
deal of any light which enters it is stopped on its way, or, 
according to the usual expression, is absorbed; and the 
greater the mass of the air through which the light has to 
come, the greater is this absorption. This explains the com- 
parative dimness of the Sun when seen near the horizon. 

52. The Sun's atmosphere, like the Earth's, absorbs much 
light ; and any part of it has undoubtedly more density and 
more absorbent power the nearer it lies to the photosphere. 
Now, when we look at the limb of the Sun, we are, in I 
looking about half-way round the photosphere from that part 
of it which seems to be in the middle of the disk to the part 
directly opposite, on the other side of the Sun. The light 
which reaches us from the limb must accordingly have pas 
along a considerable part of the photosphere through the 
denser portion of the Sun's atmosphere ; while the light from 
the middle of the disk has come to us directly away from the 
Sun, and therefore through as little as might be of its atmos- 



Sec. 52.] Suns, or Fixed Stars. 3$ 

phcre. The gradual darkening of the Sun's disk towards 
the limb is consequently due to the globular form and to the 
atmosphere of the Sun taken together ; so that it would be 
partly, though only partly, true to say that a good photograph 
of the Sun looks solid because it is actually the photograph 
Jobe. 

53. The shading upon the Sun's disk which has just been 
explained is darker in some places than in others no nearer 
to the limb. In many parts of the disk we usually see a 
mixture of brighter and darker specks, which present what 
is called a granulated appearance. The brighter specks 
have been compared to willow leaves and to grains of rice; 
a sufficient name for them, however, is that of granules. 
They differ in form at different times, and their nature is 
unknown. When a bright spot or streak large enough to 
be separately noticed appears upon the disk, it is called a 
facula. 

54. Facula? are seen for the most part near the limb, but 
not very close to it ; while the ordinary granulation is best 
seen in the middle of the disk. This may be explained by 
supposing that the matter of the facula? is no brighter than 
that of the photosphere, while the facula? lie in a region 
outside of the photosphere and considerably beyond it, 
although we need not suppose them entirely disconnected 
from the photosphere. In this case the light from the facula? 
near the limb would be much less subject to absorption by 
the Sun's atmosphere than that from the neighboring part 
of the photosphere, so that the facula? would be separately 
seen. On the other hand, near the middle of the disk the 
comparative brightness of the photosphere wouid hinder 

rom seeing the facula? separately. Close to the limb, 
Lin, the absorption of the light of the facula? may be great 
to m ike it hard to see them. The matter of the gran- 
ly also lii e the main body of the photo- 

sphere, but is connected with it more closely than the feu 
are. T e middle of the disk we can look in bet v. 

the granules and see the darker spaces among them, while 

3 



34 Outlines of Astronomy. [Sec. 54. 

we see the granules near the limb from one side, so that each 
granule hides the space between it and the granule next to it 
on the side towards the limb. In the same way, we cannot 
see the valleys among a distant group of mountains ; but we 
could, if we were in a balloon above the mountains, so as to 
look towards their tops instead of their sides. But what 
faculae and granules are, and how they are arranged, is still 
doubtful. 

55. The darker specks on the Sun's disk are perhaps 
due to masses of absorbent vapors occupying cavities or 
hollows in the photosphere. Whether the matter of the 
photosphere is liquid or gaseous, or composed of clouds of 
liquid or solid particles floating in gases, it is no doubt 10 
a very changeable and disturbed condition, with mountains 
and valleys forming and closing perpetually, like the moun- 
tains and valleys which we see in the great masses of cloud 
rising before a thunder-storm ; but these terrestrial clouds 
are of course much smaller than any which could be seen at 
our distance from the Sun. 

56. A dark speck upon the Sun's disk large enough to be 
separately noticed is sometimes called a pore. This name 
seems to imply that the speck is a hole through the photo- 
sphere ; but in fact we do not know that it is so. A large 
pore is called a macula, or more often and more simply a 
spot. The solar spots are the most noticeable objects on 
the Sun's disk, which is seldom wholly free from them. A 
spot often consists of two distinct parts : a dark central por- 
tion, called the umbra, and a lighter portion surrounding the 
umbra more or less completely, and called the penumbra. 
The umbra is not always uniformly dark. Sometimes one 
portion of it is darker than the rest ; the name of nucleus 
has been given to any such unusually dark part of an umbra. 
Sometimes a whole umbra is called a nucleus, but this is not 
a good practice. The inner edges of penumbra^ or those 
edges which border upon the umbrae of the same spots, have 
been noticed to appear brighter, at least in some places, 
than their outer parts ; and this has been thought to result 



Sec. 56.] Suns, or Fixed Stars. 35 

from the crowding together of granules moving towards the 
inner edges of penumbra from the parts of the photosphere 

around the spots to which these penumbra belong. 

57. The forms of solar spots are very various ; and a spot 
often changes its form considerably in the course of a few 
days, sometimes even in a few hours. Occasionally, how- 
ever, a spot retains for many days a nearly circular shape, a 
round umbra being enclosed in a ring of penumbra. Some 
spots consist only of penumbra, others only of umbra ; others 
have both penumbra and umbra arranged in a manner more 
or less unsymmetrical ; several umbra? are seen at times sur- 
rounded by a continuous penumbra. Spots very generally 
occur in groups ; and a group of spots is sometimes large 
enough to be seen without a telescope. Bright streaks, 
called bridges, are often seen crossing spots from side to 
side, or projecting into them upon one side. 

Solar spots are almost always more than twice as far 
from either pole of the Sun as from its equator ; but a spot is 
seldom more than eight times as far from the pole nearest to 
it as from the equator. In other words, and using the term 
latitude with regard to the Sun as geographers use it with 
regard to the Earth, the region where spots abound in each 
hemisphere of the Sun is between the tenth and thirtieth 
parallels of latitude. 

59. The rotation of the Sun causes the spots apparently 
to cross its disk from the following to the preceding limb. 
Since sometimes one and sometimes the other pole of the 
Sun is upon the disk, according to the situation of the Earth 
and Sun with respect to each other, the paths of the spots 
across the disk sometimes seem to be curved one way and 
sometimes the other. When both the Sun's poles are near 
the limb, the paths of the spots seem to be nearly straight. 
This happens early in June and December of each year. In 
March and September the paths of the spots seem most 

ngly curved, being in March hollow or concave town 
the south, and in September towards the north. It is by 
careful observation of the apparent paths of the spots upon 



36 Outlines of Astronomy. [Sec. 59. 

the disk, and by calculations depending upon such obser- 
vations, that we have been able to discover the position of 
the Sun's poles, and the time which one of its rotations 
occupies. 

60. But the spots change their places to some extent with 
respect to each other, and consequently the period of the 
Sun's rotation as determined from the movements of one 
spot will differ from that determined from the movements of 
another. As a rule, the period of rotation is found to be 
shorter when determined from spots near the equator than 
when spots far from the equator are used for the same pur- 
pose. If there were spots enough close to the equator of 
the Sun to enable us to make use of them alone in determin- 
ing the period of the Sun's rotation, they would make that 
period seem to be very little, if at all, more than 25 d, 
unless the rule just mentioned does not hold good in all p 

of the Sun. We see, then, that no one knows precisely how 
fast the main body of the Sun turns upon its axis ; for the 
only marks by which we can judge of the rate of this move- 
ment are not fixed upon the Sun. It is possible, indeed, 
that there are such currents of gas circulating about the Sun 
in the region of its spots as to make the rotation of that 
region decidedly different from the rotation of the Sun's inte- 
rior portions. Particular spots may change their places with 
regard to others, either by their drifting about under the influ- 
ence of gaseous currents, or by their irregular growth and 
dissolution ; just as a terrestrial cloud may be blown along 
by the wind, or may seem to change its place because one 
side of it melts away and the other increases. These char, 
of places of solar spots are called their proper motions. 

61. A group of spots is generally more or less surrounded 
and interspersed with faculae ; and solitary spots often have 
faculae in their neighborhood. The faculae preceding (49) 
spots are apt to be smaller and fewer, but brighter, than 
those which follow ; and the largest umbra in a group of 
spots is apt to be on the preceding side of the group. When 
a circular spot is near one of the limbs, it looks oval instead 



Sec. 6 i.] Suns, or Fixed Stars. 37 

of round, so that when it is close to the limb it seems like a 
dark line drawn along the limb. This is an effect of per- 
spective, like that which makes a window seem narrower 
when we look along the side of the house it belongs to than 
when we stand opposite to it. But besides this, the penum- 
bra of a spot near the limb often seems to lie between the 
umbra and the limb, while when the spot is in the middle of 
the disk the penumbra is seen all round the umbra. Observa- 
tions of this kind gave rise to a theory that an umbra is the 
bottom of a pit in the photosphere, the sides of which appear 
as a penumbra. But this theory is now less in favor than it 
was ; and in a small book like this there is no room for an 
account of the different suppositions about solar spots which 
have been formed or renewed in recent times. The preva- 
lent belief is that a spot is an appearance due to a mass of 
gases comparatively cool and having much power of absorbing 
light, which accordingly darkens that part of the photosphere 
between which and the Earth it lies. These gases very 
probably occupy some kind .of hollow in the photosphere. 
A spot can be said to be dark only by contrast with the sur- 
rounding photosphere, much as a wire heated red hot in a 
bright flame is dark by contrast with the flame, and looks 
black when held between the flame and the eye. The dark- 
est part of a solar spot is probably brighter than any incan- 
descent terrestrial object. 

62. The rotation of the Sun prevents any spot from remain- 
ing in sight more than about a fortnight at a time. But after 
passing out of sight on the preceding limb, spots often last 
long enough to reappear on the following limb ; and they 
have been known to outlast eight or nine rotations of the 
Sun. Of course, however, it cannot be known that spots 
have not closed up or dissolved and new ones been formed 
in the same neighborhood while that part of the photosphere 
in which they occur has been turned away from the Earth. 
It often happens, in fact, that after a spot upon the disk lias 
dwindled away entirely, a new spot is formed somewhere near 
the place of the old one. 



38 Outlines of Astronomy. [Sec. 63. 

63. The average number of spots visible at once varies 
from time to time. A maximum of spots is said to have oc- 
curred at any time when the spots were more abundant than 
they were for some seasons before or after ; and a minimum 
of spots occurs when spots are comparatively very scarce, 
that there are often days when no spots can be seen. A max- 
imum of spots occurs about once in every eleven years ; but 
two maxima are not always just eleven years apart. I 
example, there was one maximum in 1848 ; the next did not 
come till i860; and the next came in 1870. A minimum 
spots usually comes not half-way between two maxima, but 
rather nearer the maximum that is to come next than to the 
previous one. For example, the minimum between the max- 
ima of i860 and 1870 came early in 1867. About the time 

a minimum the spots on the whole lie nearer the Sun's equa- 
tor than usual. 

64. Besides this period of eleven years, there is another 
longer period of variation in the numbers of the solar gp 
But the spots have not been carefully observed for a sufficient 
time to determine the exact length of this long period. It 
apparently occupies five of the short periods. 

65. The reason why spots are more abundant at one time 
than at another is still unknown. There are some grow 
however, for thinking that any large object, like a planet, not 
too far from the Sun, tends to diminish the spotted area of 
that part of the photosphere nearest it, and perhaps to in- 
crease the spotted area on the opposite side of the Sun. 

60. The photosphere is too bright to allow us to see much 
of what goes on in the Sun's atmosphere between us and the 
disk. Even round the limb, where there is of course much 
of this atmosphere which has not the disk behind it, an ordi- 
nary telescope is prevented by the sunlight which our own 
atmosphere reflects and scatters in all directions from show- 
ing us any thing remarkable in the atmosphere of the Sun. 
But this difficulty has been overcome by the invention of the 
spectroscope, an instrument which can be so applied to a tel- 
escope as to enable us to learn much about the Sun's atmos- 



THE SUM. 



Plate J. 




The number of prominences represented around the disk of the Sun 
in the above view is probably much greater than the number of promi- 
nences ever actually visible at one time ; but the form and height of 
each prominence are derived from actual observation. The granula- 
tion shown in the figure is coarser than that which is usually seen. A 
few faculae appear near some of the spots close to the limb ; and the 
two zones of spots are shown. 



r» f • 



(ft 
A p 





TanpwuftRaiiuav ' iih 



The cumulation of the photosphere, and the umbrae, penumbrx, 
and bridges of solar spots, are shown in this figure. 



Sec. 66.] Suns, or Fixed Stars. 39 

phere even when the disk is behind the part of it at which we 
look ; and still mure about it as it appears around the limb. 
In this way its chemical constitution has been to some extent 
discovered, as was said above (32). 

67. Close to the photosphere, and everywhere enveloping 
it, there seems to be a layer of atmosphere consisting of vast 
numbers of metals and other substances in the form of gas. 
The matter ot which the photosphere consists may be float- 
ing in this atmosphere (32), which may therefore not merely 
surround the photosphere, but be mingled with it. The heat 
of the Sun, then, is so intense that it keeps substances like 
iron not only melted, but actually boiling, all around it. Out- 
side of this innermost shell of solar atmosphere is another in 
which many metallic gases exist, as well as others, although 
they are not at all times hot enough to give out light of their 
own. This part of the Sun's atmosphere has been called the 
chromosphere. Incandescent hydrogen gas seems to exist 
everywhere in the chromosphere, extending here and there 
as much as a fifth part of the Sun's whole thickness, or, in 
other words, over a hundred and fifty thousand miles, beyond 
the photosphere. Mountainous projections of the chromo- 
sphere of this kind, though not always so large, are called the 
Sun's prominences or protuberances. Other gases than 
hydrogen can often be perceived in these prominences, espe- 
cially in such as have the form and appearance of jets of 
flame rather than of mountains, clouds, or wreaths of smoke. 
The whole chromosphere, as seen around the limb of the 
Sun, has usually a jagged or serrated outline, as if it were 
coated with small prominences, as a field is covered with 
blades of grass. But the smallest of these projections which 
can be seen from the distance at which we observe them 
must of course be many times larger than the great moun- 
tains of the Earth. 

68. Magnesium, in the state of incandescent gas, is one 
of the chemical elements most frequently perceived in the 
chromosphere and its prominences, and is sometimes appar- 
ent around all or almost all of the Sun's limb. It would be 



40 Outlines of Astronomy. [Sec. 68. 

useless to enumerate the other substances proved or sus- 
pected to form part of the chromosphere, since our notions 
of its constitution are very imperfect and constantly liable to 
change in consequence of new observations. 

69. The solar prominences are of a very great variety of 
forms, as appears from any of the drawings which have been 
made of them. Portions of the matter of the chromosphere 
are often seen detached from the remainder and Moating in 
the atmosphere around it, or sinking towards it. Prominen 
often change their forms very rapidly, and even appear to 
explode and suddenly become dispersed into fragments ; 
some, however, remain nearly unchanged for many days at 
a time. Prominences of a particular kind, the appearance 
of which seems to indicate that they have been formed by 
eruptive action, are found to be associated with facula? ; or, 
as some say, are facuke themselves. That is, when the rota- 
tion of the Sun carries a facula olf the disk, a prominence 
this particular kind is generally seen on that part of the 
limb which the facula is presumed to be crossing. In the same 
way, the appearance of a facula which the Sun's rotation 
brings upon the disk is preceded by the appearance 1 
prominence of this particular kind on that part of the limb 
crossed by the facula. 

70. It is commonly believed, although it is not yet pi 
that by the use of the spectroscope, astronomers are often 
enabled to learn which way the objects they observe are 
moving, and even to estimate their speed. Certain spectro- 
scopic observations have been thought to show that some of 
the solar prominences are whirlwinds of fiery gas. The J 
on one side of such a whirlwind must of course be coming 
towards the observer, and on the other moving from him, 
provided that he is looking across the whirlwind and not 
along its axis. For instance, when we look down upon a 
spinning top, each part of it perhaps keeps always at about 
the same distance from us ; but if the top is on a table, then 
the part of the top on the left hand of a person sitting before the 
table is coming towards him and the opposite part going 






Sec. 70.] Suns, or Fixed Stars. 41 

from him, if the string was wound in the usual way. The 
speed with which the whirling' prominences are thought to 
turn is sometimes so great that their outer parts are carried 
more than a hundred miles in a second ; and the movements 
of parts of protuberances of other kinds, especially when 
they seem to be scattered by some sort of explosion, are as 
quick, and even quicker. It is not certain, however, that 
the facts which have given rise to the belief in these move- 
ments have been correctly understood. 

71. Before spectroscopes were invented, the prominences 
could only be seen during total eclipses of the Sun, when 
its disk is behind the Moon for a few minutes. At such times 
any large prominences which are then situated on the limb 
of the Sun can be seen without the help of instruments. 
Their color is usually pale red, or reddish yellow. This is 
because the strongest part of the light sent out by incan- 
descent hydrogen is of a particular shade of red, and most of 
the light from the prominences is the light of incandescent 
hydrogen. When seen in the spectroscope, the prominences 
may be made to appear red, yellow, or blue, according to the 
manner in which the instrument is used. But it is most con- 
venient to use it so as to make them appear red. 

72. The prominences and faculae are on the whole most 
numerous and brilliant in the same parts of the photosphere 
where the spots are most abundant (5S) ; but they are not so 
strictly confined to these regions as the spots are, sometimes 

en near the poles of the Sun. Attempts have been 
made to determine, by means of facuke and prominences, the 
rate of the rotation of parts of the photosphere beyond the 
spotted region ; and so far as any thing has thus been made 
out, it would seem that the period of rotation is not far from 
ys for any part of the photosphere. 

73. Part of the Sun's atmosphere certainly lies outside of 
the chromosphere ; but no way has yet been found out in 
which this outer atmosphere can be examined except during 
the few minutes of a total eclipse. Little, therefore, is known 
about it, although a great deal has been imagined about it. 



42 Outlines of Astronomy. [Sec. 73. 

We are not yet certain how much of the light seen round the 
Sun during its total eclipses really comes from its atmos- 
phere. This light is called the corona. It has often been 
photographed during total eclipses, and the pictures thus 
obtained at different times and places have enough like;. 
to each other to show that at least the inner parts of the 
corona actually belong to the Sun's atmosphere, or to some 
kind of shining matter surrounding the Sun and keeping 
about the same shape. Near the poles of the Sun there is 
comparatively little of this shining matter, and although 
there is more of it about the Sun's equator, it is most abun- 
dant in places between the poles and the equator, resembling 
in this respect the spots, facuke, and prominences. It shines 
by light of its own, so that the corona does not wholly con 
of sunlight reflected from gases or other kinds of matter (8). 
In some photographs of the corona, it appears to consist 
of two or three different masses of light mingled together, 
but distinguished by their differences of brightness. The 
innermost part of the corona appears as a ring of bright 
light, close to the limb, and not reaching farther from it 
than the prominences sometimes do. This, no doubt, belongs 
to what we may properly call the atmosphere of the Sun. 
As to the rest of the corona, so far as it is not occasioned 
by the Earth's atmosphere, no one knows yet whether it is 
due to an incandescent atmosphere of the Sun ; to electrical 
action ; to matter thrown out of the Sun, as our volcanoes 
throw out flame, smoke, and ashes; or, finally, to matter mov- 
ing about in the Sun's neighborhood, but not to be regarded 
as forming any part of the Sun. All these suppositions have 
been made, but we must wait for much more knowledge of 
the Sun than we have now before we can say whether any of 
them are correct. 

74. The heat of the Sun, like its light, is to a considerable 
extent absorbed by its atmosphere ; so that the heat we 
from any part of the photosphere depends on its distance 
from the limb at the time. Besides this, it has been found 
that the region about the Sun's equator is somewhat hotter 



Sec. 74.] Suns, or Fixed Stars. 43 

than regions nearer its poles. Other differences of temper- 
ature in different parts ot the Sun have been suspected, but 
are not known to exist. 

7«>. How the Sun came into its present condition, and 
how that condition is to change hereafter, if it changes at all, 
are questions on which much has been said and written ; 
but they cannot be settled at present, and none but good 
mathematicians are really able to understand the arguments 
which there are for holding one opinion or another on any 
such question. We have no means as yet of knowing 
whether the Sun is growing larger or smaller, brighter or 
fainter, hotter or cooler. We cannot even determine accu- 
rately how much heat and light it sends us now, or how its 
heat and light compare with those of other celestial objects. 
:h progress has been made, however, in inquiries of this 
kind ; and probably men will some day be able to follow the 
course of the Sun's changes so as to foresee what changes 
are to come next. What is certain now is that no changes 
have occurred in the Sun for several thousand years so great 
as to alter noticeably the condition of mankind. 

76. We can determine the size of the Sun somewhat more 
accurately than we can determine the amount of its heat and 
light. Still, owing to the difficulty of deciding where the 
body of the Sun ends and its atmosphere begins, and to 
the stormy and unsettled condition both of the photosphere 
and chromosphere, we cannot measure the Sun with great 
precision, and some observers have fancied its shape to be 
somewhat irregular, and not that of an exactly uniform globe, 
or. in other words, of a sphere ; while most astronomers 
think that so far as can be seen the Sun on the whole is 
:tlv spherical. On account of this uncertainty of meas- 
urement, the Sun might actually grow larger or smaller for 
a long time before the fact could be discovered. If it is 
growing hotter, we should expect that to make it 
but, on the other hand, its shrinking would keep Up its heat, 
or even increase it. Its enlargement by the addition of 
matter from the surrounding parts of the univcr.se might tend 



44 Outlines of Astronomy. [Sec. 76. 

to heat it, but might also give rise to effects of an opposite 
tendency within it. On the whole, then, when we see one 
theory or another advanced with regard to the future history 
of the Sun, it is safest to remember that the theory cannot, 
in the present state of human knowledge, be any thing more 
than a guess. 

77. If other suns than that which has just been described 
could be thoroughly compared with it by means of astronom 
observations, we might be able to answer some of the qu 
tions mentioned above. But the great distance of the other 
suns (24) makes it difficult for us to study them at all, and 
what we know of them is little more than their resemblance 
in some important particulars to the Sun of our own system. 
Every Object commonly called a star seems to be one of 
these suns, except those stars the motion of which, with 
respect to the others, can be easily perceived by at BKM 
few days' observation. It will be convenient, then, to use 
the word star only when we intend to speak of a sun. A 
shooting star, a morning star, or an evening star, is n. 
star at all in this sense of the word : shooting stars are 
meteors, and the objects called morning and evening stars 
are planets. 

78. The number of stars which can be seen without the 
aid of any instrument depends of course on the strength of 
the observer's eyesight and the climate o\ the place where 
he is. The number of stars which can be seen from well 
situated places in the southern hemisphere of the Earth 
seems to be decided!) than the number visible from 
its northern hemisphere. Perhaps we ought to allow that as 
many as ten thousand stars may be seen by sharp-sighted 
people. But wherever we stand, the Earth cuts off our \ 

of about half the universe at any one time, so that not more 
than about five thousand stars can be in sight at once. In 
most parts of the northern hemisphere, persons with ordi- 
nary eyesight probably cannot see more than 2000 of the 
stars above their horizon at any particular time. Manv mil- 
lions of stars can be seen with the help of powerful tele- 
seopes. 






Sec. 79.] Suns, or Fixed Stars. 45 

79. The difference in brightness which we notice between 
different stars may be occasioned either by their different 
distances from us or by an actual difference in size or bril- 
liancy between the stars themselves. As we know the dis- 
tance of very few stars, we cannot usually tell whether a 
bright star is larger than a faint one, or actually brighter, or 
only nearer to us. But on the whole, if bright and faint stars 
are evenly distributed through the universe at different dis- 
tances from the Earth or any other object from which we 
choose to measure, then the effect must be practically the 
same as if the stars were all equally bright. That is, if we 
divide the stars according to their brightness into groups 
equally large, each containing some great number of stars, 
that for instance the first group contains a thousand stars 
the faintest of which is as bright as any star not belonging to 
the group, while the second group takes in a thousand stars 
the faintest of which are as bright as any not belonging to 
either the first group or the second, and so on ; then it will 
be reasonable to suppose that the average distance from the 
Earth of the stars in any group will be greater than the aver- 
age distance of the stars in any brighter group. In any 
actual grouping of the stars on this system we should make 
each successive group include more stars than that preced- 

it, for reasons which will be obvious to any one who is 
acquainted with geometry. 

HO. We know nothing of the bulk or size of any star 
except the Sun. But some notion has been gained of the 
masses of a few stars. The star Procyon, for example, is 
thought to have a mass eighty times as great as that of the 
Sun. If its bulk is proportionately great, its thickness must 
on geometrical principles be nearly four and a third times 
that of the Sun, and over four hundred and sixty times that 
of the Earth. There is nothing unlikely in this, but it cannot 
be proved, since Procyon. like the other >tar^. bright or faint, 
k which we can measure. One proof of the 

1 quality of a telescope is its making the stars look 
smaller, not larger, than they seem with a wor.^c instrument. 



46 Outlines of Astronomy. [Sec. 80. 

The apparent disk of a star is only a blur of light which is 
reduced to a little dot by a good telescope when the air is 
clear and quiet. No star, even if it were considerably nearer 
to us than the nearest yet known, could show us a real disk, 
by measuring which we could learn the bulk of the body 
to which it belonged, unless its thickness was at least thirty 
or forty times that of the Sun. If there are any stars much 
over one hundred times as thick as the Sun, they are not 
among those which are nearest to us ; and this is all which 
we know of the bulk of the stars. 

81. But in spite of this, a bright star always looks larger 
than a faint one, just as a bright Maine would look larger than 
a faint flame which was really of the same size with it. 
Hence astronomers speak of the magnitude of a star when 
they really mean its brightness. The stars which can be 
seen by ordinary eyes without any instrument are divided 
into six magnitudes. That is, a few of the brightest sf 
although they diiTer much in brightness from each Other, are 
all said to be stars of the first magnitude ; then a l.i 
number of stars, somewhat fainter than those of the first 
magnitude, are called stars of the second magnitude ; the 
stars of the third magnitude are still more numerous and 
fainter ; and we may ^o on classifying the stars in this way 
as long as we choose. Any telescope, even a small opera- 
glass, will show us many stars fainter than the sixth magni- 
tude, and the better our telescopes are the more magnitudes 
of stars come into view, so that with the best instruments 
now made about twenty magnitudes of stars can be seen. 
After the first few of these classes, called magnitudes, have 
been formed, there is no difficulty in finding stars enough, all 
about equally bright, to make up each succeeding magnitude. 
But of course there are many stars, however we arrange our 
magnitudes, which will belong as much to one of two succes- 
sive magnitudes as to the other. For instance, a star may 
be rather fainter than most of those called sixth magnitude 
stars, and yet rather brighter than an average star of the 
seventh magnitude. This does not prevent the classification 



Sec. Si.] Suns, or Fixed Stars. 47 

of stars into magnitudes from being convenient for many 
purposes ; and when a star comes between two magnitudes, 
its degree of brightness may be indicated by naming both 
magnitudes. Thus a star of the magnitude 2.3 is between 
the second and third magnitude, but nearer the second than 
the third ; while the magnitude 3.2 is nearer to the third 
than the second magnitude. In this way of writing magnitudes 
the dot is not a decimal point, but only separates the two 
figures. Sometimes, however, astronomers divide their mag- 
nitudes into tenths, so as to have ten times as many classes 
of stars as there are in the system just explained ; and then 
a star marked 3.2 would be one belonging to the magnitude 
three and two-tenths, or in other words, fainter than a third 
magnitude star, not brighter, as it would be according to the 
other system. 

82. Most stars of the first magnitude, and many of the 
second and third magnitudes, were named by ancient ob- 
servers. Besides naming particular stars, early astronomers 
also gave names to groups of stars, called constellations. 
In course of time, however, constellations came to mean 
rather regions of the sky than groups of stars, just as a state 
means in geography rather a piece of land with certain boun- 
daries than the people who live there. Many of the names 
both of stars and of constellations which are now in common 
use in the English language were originally Latin or Greek 
words ; but several of the stars have names derived from the 
Arabic. Particular stars are often denoted only by the names 
of their constellations, with numbers or letters from the 
Greek or Roman alphabet prefixed, in order to distinguish 
between stars of the same constellation. But in modern 
times the place in the sky in which any star is seen from 
the Earth can be so briefly and accurately stated, that we 
can often dispense with any names for stars except the 
figures which point out these places. The first magnitude 
stars most familiar to people living about half-way between 
the north pole of the Earth and its equator are as follows : 
they may be divided into two groups, according to the time 



48 Outlines of Astronomy. [Sec. 82. 

of year at which they are most likely to be noticed. But the 
place where any star is seen changes with the time of day as 
well as with the time of year. 

a. Stars chiefly visible in winter evenings. Sirius. the 
brightest of all first magnitude stars, is seen in the south- 
east early in January evenings. As the season advances, it 
is seen more towards the west at the same time of day, and 
late in spring we lose sight of it in the south-west. N 
Sirius, and north of it, but farther west, is the constellation 
called Orion ; its brightest stars, Rigel and Bctelgeux, are of 
the first magnitude. Rigel is bluish white, like Sirius, and 
is in the southern part of the constellation ; Betelgeux is red- 
dish, and farther north. Apparently not far from this star, 
and somewhat west of it. Is another red first-magnitude star, 
Aldebaran. Procyon seems rather more distant from P>< 
geux than Aldebaran is. and in the Opposite direction ; it 
forms one corner of a great diamond-shaped figure, with 
Sirius. Rigel, and Betelgeux at the other corners. Capella 
lies considerably to the north of Aldebaran and Betelgeux. 
It is brighter than any of the stars just named except Sirius. 
East of Capella are two rather bright stars, Castor and Pol- 
lux. Pollux is the brighter of the two; Castor is hardly 
bright enough to count as a first magnitude star. Regulus, 
a star still farther east, visible later in winter evenings, is 
also faint for a star of the first magnitude. 

b. Stars chiefly visible in summer evenings. The 
brightest of these is Vega, which is seen in autumn even- 
ings nearly overhead ; earlier in the season it appears in the 
north-eastern sky. It is as bright as Capella, or brighter. In 
the same region of the sky is Arided, a star about as bright 
as Castor or Regulus. Arcturus seems farther south and 
farther west, in autumn evenings, than Vega ; in the even- 
ings of spring it must be looked for in the north-east. Its 
color is slightly reddish. Spica is farther south than Arctu- 
rus. It is seen in early summer about where Sirius is seen 
late in winter. Altair is south of Vega and east of Arcturus. 
It is the middle star of three in a line with each other. An- 



Sec. 82.] Suns, or Fixed Stars. 49 

tares is a reddish star seen low in the south in the evenings 
of July and August ; and Fomalhaut appears in about the 
same quarter in autumn. 

The remaining stars of the first magnitude, Canopus, 
hernar, and three stars in the constellations of the Cen- 
taur and the Cross, are at present always out of sight from 
places on the Earth far north of its equator. 

84. It is not difficult, since there are so few stars of the 
first magnitude, to learn to recognize all which come in sight. 
They are most easily distinguished early in the evening, or 
by moonlight, when none but bright stars can be seen. 
Those which are ill sight on any clear evening can then be 
guides in finding the names of other stars by the help 
of a globe or map ; but unless some stars are already known, 
it is often troublesome for a beginner to learn the use of 
maps of the sky. 

S$. Planets may be mistaken for stars of the first magni- 
tude until they have been watched long enough to discover 
their movement among the stars ; but no planets seem to 
pass near any stars of the first magnitude except Aldebaran, 
Castor and Pollux. Regulus, Spica, and Antares. 

86. Regulus, Arcturus, Spica, Fomalhaut, and Achernar, 
as seen from the Earth, do not seem to lie near the Milky 
Way. as do all the other stars of the first magnitude. 

87. The name of the Milky Way, or Galaxy, is given to 
a whitish strip or belt of the sky, one part or another of which 

generally in sight on any evening when the Moon is not 
too bright. The Milky Way is much wider in some parts 
than in others ; and its outline is irregular. It is made up 

great numbers of little stars, too small to be seen separately 
without a telescope. Not only stars of the first magnitude, 
but al^o other bright stars, are more abundant in those re- 
gions of the sky crossed by the Milky Way than they are 
elsewhere. 

88. The subject of the arrangement of the stars in the sky, 
especially with reference to the Milky Way, has occupied the 
attention of many astronomers. Attempts have been made 

4 



50 Outlines of Astronomv. [Sec. 88. 

to determine the shape which the whole group of visible stars 
taken together would have to observers who could look at 
that group from the outside instead of from a place within it 
like the Earth. But no satisfactory conclusion has yet been 
reached, although a theory long prevailed that the group is 
shaped somewhat like the letter Y, the place of the Sun being 
in the stem of the letter, near the fork. But this is doubtful. 
811. Here and there in the sky, but chiefly in the Milky 
Way, and near it, we see stars forming clusters ; and it is 
reasonable to suppose that the stars of each cluster form a 
system (24), although each of these stars is very probably 
the chief member of a smaller system. But we cannot feel 
sure that all the stars of each cluster belong to the same E 
tern, because two stars may be seen nearly in the same part 
of the sky. and yet one may be many times as far from u- 
the other is, just as the tops of two hills often stem dose 
together when we are at some distance from them, but far 
apart when we have climbed the Dearest of them. The St 
of any cluster which can be seen without a telescope must be 
very far from each other to be seen separately at all ; still, 
such clusters, or parts of them, may really be \ 
One of the most familiar clusters of this kind is that called 
the Pleiades, visible near Aklebaran. Six stars can be seen 
in this group by most people, and ten have been seen by 
unusually good eyes. But even a small telescope will show 
many more. Aklebaran itself is the chief star of another 
group called the Hyades. Between Pollux and Regains is 
another cluster called Pra?sepe, which looks like a whitish 
speck in the sky, its separate stars not being seen without 
a telescope. But the most remarkable clusters are some 
which can only be seen with good instruments. In th< 
hundreds and even thousands of stars seem to be gathered 
together into sparkling heaps, like the little crystals in a 
handful of snow. We can scarcely doubt that such clusters 
are really systems ; and some have thought that they might 
lie entirely outside of the great group to which the Sun and 
the brighter stars, as well as those of the Milky Way, have 



Sec. 89.] Suns, or Fixed Stars. 51 

been supposed to belong. Sometimes this group has been 
called our universe ; and the clusters thought to lie outside 
of it have been spoken of as separate universes : but this is a 
confused wa\ iking, even if there are such outlying 

clusters, and we do not know that there are. 

1M). We should be sure that the stars of a cluster really 
belonged to the same system if we saw them gradually move 
among each other in such a way as to show that the move- 
ments of each depended more on the places of the others 
with respect to it than on the places of stars outside of the 
cluster. But such movements would be so intricate that 
we could not well understand them if they had been seen ; 
and tiie places of stars belonging to clusters have not yet 
been observed accurately for a sufficient" number of years 
show us what changes occur in them. But when two 
or three stars only seem close together in the sky, it 
often happens that by watching them for a few years we 
can tell how they move with respect to each other ; and 
we already know of several systems, each consisting of two 
or three suns. It is likely enough that these suns have many 
planets near them and belonging to their systems ; but this 
is uncertain. 

91. When two stars seem so close together that they 
appear as one star until the distance between them is con- 
siderably magnified by means of telescopes, they are said to 
form a double star. A double star is optically double, when 
the two stars which compose it are really far apart, and only 
seem near because one of them lies nearly between us and 
the other. When they belong to one system, they form a 
physically double star, or, as we often say, a binary star. 
Sometimes, but seldom, a star is said to be double even 
when we need no telescope to separate it into two. A rather 
faint star seen near Vega, for instance, appears double to many 
people. A crood telescope shows that each of the two stars 
which make it up is itself double, .and that there are several 
faint stars between the two pairs. The whole group is some- 
times spoken of as a double-double star. We also speak of 



52 Outlines of Astronomy. [Sec. 91. 

any three stars seemingly near each other as a triple star ; 
a close group of four stars may be called a quadruple star ; 
and any close group of stars may be called a multiple - 

92. The separate stars which make up a double, triple, 
quadruple, or multiple star, are called its components ; and 
the fainter components of such a star are generally called 
the companions ot the brighter. Sirius and Procyoa have 
faint companions, which are interesting, because they stem 
to have more effect on the movements of the stars they ac- 
company than we should expect. Hence, these faint stars 
have been supposed to be in reality large bodies, but com- 
paratively dim ones. The companion of Procyon is thought 
to have seven times the mass of our Sun. The mass of a 
star can be calculated only by means of the observation of its 
movements with respect to some other star of the same B 
tern with it. In such calculations our distance from the stars 
observed must be taken into account. 

93. All the stars, we may take for granted, are governed 
in their movements by each other's places and masses ; but 
the general movements among them which are brought about 
in this way must be far too complicated tor us to comprehend 
at present. All that has yet been learned about these move- 
ments relates mainly to the way which the Solar system is 
moving; and all we know of this particular movement is that 
at present it is towards those stars which belong to the con- 
stellation (82) Hercules. There has been some speculation 
about a supposed revolution of various stars, including the 
Sun, about some centre near the Pleiades. But on this 
subject we have as yet no knowledge. The movement 
which each star seems to have in the sky among the other 
stars is called its proper motion. These proper motions 
are slow, however quick the actual movements of the stars 
may be, because we look at them from so great a distance. 
Thousands of yearls must pass before the general appearance 
of the evening sky can be changed by the proper motions of 
the stars. 

94. If the spectroscope shows us any thing of the move- 






Sec. 94.] Suns, or Fixed Stars. 53 

ments going on upon the Sun, we may expect it to show 
something of the actual movements of other stars with 
respect to the Sun ^70). By spectroscopic observations, 
the conclusion as to the movement of the Solar System 
already derived from the proper motions of the stars has 
been confirmed. Arcturus, for instance, appears to us near 
the constellation Hercules, while Sirius lies on the opposite 
side of the Solar System. Some astronomers who have 
studied these stars with the spectroscope inform us that 
the distance between Arcturus and the Sun is lessening, 
while the distance between Sirius and the Sun is increasing 
at the rate of from 10 to 30 miles in a second. But Sirius, 
like the other stars, is so far from us, that its distance may 
continue, and, perhaps, has continued to increase at this 
rate for centuries, while its brightness remains seemingly 
unchanged. Some time or other, however, if the space 
between Sirius and the Solar System constantly grows 
larger, we may presume that the star will seem faint to 
terrestrial observers, and finally disappear from their sight. 
It must be remembered that we know at present only that 
certain observers have concluded its distance to be increasing 
at the time of their observations, not that it has always been 
increasing. 

95. Observations with the spectroscope have also con- 
firmed the belief previously grounded on the brightness 
and remoteness of the stars, that they are bodies resembling 
the Sun (28). It has been shown that, like the Sun, they 
have photospheres surrounded by atmospheres capable of 
absorbing light of certain kinds ; and that there is reason 
to think that in many ways their chemical properties are like 
those of the Sun and of terrestrial bodies. In particular, 
believed to form part of the atmosphere of 
many stars besides the Sun ; and around some brilliant white 
irius, hydrogen is thought to be very abundant in 
condition. So ne reddish stars, again, 
have been supposed to show by the nature of their light that 
their photospheres are more spotted than that of the Sun. 



54 Outlines of Astronomy. [Sec. 95. 

But the use of the spectroscope in astronomy is too recent 
to allow us as yet to draw many positive conclusions from 
the numerous and interesting observations made with it. 

96. Without the spectroscope, we can see no difference in 
the light of different stars, except their differences of color, 
which are not striking enough to attract much attention from 
ordinary observers. Some stars, however, visible only with 
the aid of telescopes, are said to have very brilliant colors. 
A cluster in the constellation of the Cross is described 
Sir J. F. W. Herschel as containing eight stars colored with 
various shades of red, green, and blue, so as to give the 
whole group the appearance of a rich piece of jewellery. The 
components of many double stars are described as brightly 
colored ; this may be partly, but is not wholly, the effect 
of contrast between the tints of objects seen close to each 
other. 

97. Notwithstanding the distance of the stars, the heat we 
receive from them is in many cases enough to be measured ; 
and it is likely that if no heat came to us except from the Sun, 
the temperature of the Earth would be much lower than it is. 
But the heat received from any one star of even the first 
magnitude is of course trifling. More observations than have 
yet been made of the heat of the stars are needed before our 
knowledge of its amount can be considered exact. Measure- 
ments of this kind are made with delicate electrical instru- 
ments called thermopiles, which are attached to telescopes 
when used to determine the heat received from stars. 

98. The brightness, or, in other words, the magnitude, of 
certain stars varies from time to time. Such stars are called 
variable. Their changes sometimes extend over many v 
and in other cases are completed in a comparatively short 
time. One of the most interesting variable stars 

in the constellation Perseus. It is ordinarily a star of the 
second magnitude ; but at intervals of nearly 2\ days it 
diminishes to the fourth magnitude and again increases to the 
second, these changes occupying about seven hours on each 
occasion. Since 2-J is contained not quite 7 times in 20, 






Sec. 9S.] Suns, or Fixed Stars. 55 

it follows that if Algol is noticed to be faint on any even- 
ing, it will again appear so on the twentieth following evening. 
But as this calculation is not strictly accurate, it will not 

serve for many repetitions of the star's variation. A more 
prec ment is given near the end of this work. The 

frequency of the variation of Algol, and the tact that it is never 
so faint as to be invisible, while its changes are still great 
enough to be easily perceived, enable every one to see for 
himself that it really varies. It appears from the northern 
hemisphere of the Earth in autumn evenings in the north- 
eastern part of the sky, and may be found without much 
trouble by means of any map of the stars. 

99. Mira, the first star which was discovered to be vari- 
able, cannot be seen without a telescope when it is faintest, 
but is even brighter than ordinary second magnitude stars at 
the time of its greatest brilliancy. But as it is over 331 days 
in going through its changes, they are not so readily notice- 
able as are those of Algol. 

100. A variable star in the constellation Argo, which is 
surrounded by a nebula, and has attracted much attention 
from astronomers, is sometimes of the first magnitude. The 
course of its changes has not yet been fully made out. This 
star is not in sight from places on the Earth far north of its 
equator. Betelgeux, one of the first magnitude stars above 
mentioned, is variable ; but it never becomes as faint as an 
ordinary star of the second magnitude. 

ior. The cause of these changes in the brightness of stars 
is unknown. One of the most likely conjectures with regard 
to them is that they result from the periodical interposition of 
dark bodies of some kind, such as planets, or swarms of 
meteors, between us and the stars which appear variable. It 
has been th that the regular recurrence of the 

maxima of solar spots ( r, 3) may make it proper to consi 
the Sua a slightly variable star; and other stars may \ 
more from similar can- 

10*2. Stars have occasionally appeared where none, or, at 
all events, where none nearly as bright, had before been seen, 



56 Outlines of Astronomy. [Sec. 102 

and after a time have disappeared again. Such stars are 
usually called temporary. There is no record of the ap- 
pearance of any star which afterwards continued permanently 
bright. Temporary stars may be only variable stars with 
long intervals between their periods of greatest brightm 
The brightest of all recorded temporary stars, which was for 
a short time far brighter than Sirius, and could be seen in 
the daytime, made its appearance in 1572 near the constella- 
tion Cassiopeia, disappearing altogether early in 1574. It 
has been suspected to be the same object which produced 
similar appearances in that part of the sky in the years 945 
and 1264. If this suspicion is well founded, it should ap] 
again before the close of the present century. 

103. On the other hand, a faint star in the constellation 
Corona Borealis appeared rather bright in 1 866, and ol 
vations of it made at that time with the spectroscope v. 
thought to show that its brilliancy was due to the existence 
about it of incandescent hydrogen in unusual quantities. A 
conflagration of this kind, if the expression is allowable, may 
not return at any regular intervals, and any star the magni- 
tude of which thus is irregularly altered would not perhaps 
be properly described as variable. 

104. The colors 0/ stars may vary as well as their magni- 
tudes. Sirius, for example, was called a red star by early 
observers, but is certainly not red now. The temporary star 
of 1572 changed its color repeatedly before it disappeared. 

105. Although our knowledge of the stars is still scanty, 
the observation of their apparent arrangement in the sky has 
been the means of giving us a great deal of information 
about the Earth itself, and the large bodies comparatively 
near it. It often happens in many studies, as in the study of 
the stars, that when we do not succeed in learning much at 
once about the subject which we directly inquire into, we 
yet find the little which we can learn about it useful to us in 
other pursuits and in ways which we could not have guessed 
beforehand. 

106. The twinkling, or scintillation, of the stars is occa- 



. 



Sec. 106.] Suns, or Fixed Stars. 57 

sioned by the Earth's atmosphere, through which their light 

comes to us. It depends on the fact that the stars are too 
far from us to show us any disks, but the exact nature of the 
variations ot light called twinkling is not known. The air 
• >rbs starlight as well as sunlight, so that a star near the 
horizon twinkles more and looks fainter than one of the same 
magnitude higher in the sky. The larger planets twinkle less 
than ordinary stars, because they show us disks, although 
these disks are too small to be recognized without a tele- 
scope. 



58 Outlines of Astronomy. [Sec. 107. 



CHAPTER V. 

PLANETS. 

- 107. The name of planet3, as has be^n said (2S), is 
given at present only to certain bodies belonging to the Solar 
System (24). These bodies resemble each other in the fol- 
lowing ways. 

a. We see them by means of the sunlight which they re- 
flect, not by light of their own. It is possible, indeed, that 
a few of them may be incandescent to some extent ; but even 
if this is the fact, there are probably clouds surrounding these 
planets which cut off from us most if not all of their light ; 
so that the light which they send us is mainly sunlight re- 
flected from their clouds. 

b. They never change their distance from the Sun very 
greatly ; that is, no one of them is much over twice as far 
from the Sun at one time as at another. 

c. They seem to be compact bodies, and not mere clouds 
of dust or vapor. Indeed, none of them are commonly sup- 
posed, like the Sun, to be in the state of gas, however con- 
densed ; but several of them may be mainly liquid bodies. 

108. In many respects, and especially in size, the planets 
differ greatly^from each other. A few of the largest of them 
are known to be globular in shape, like the Earth ; the rest 
are so small that they appear like faint stars, and show us no 
disks by which we can judge of their shape and size. The 
bulk of such planets can only be imperfectly estimated by the 
consideration of their distance and brightness ; their shapes 
are unknown ; and their masses cannot usually be separately 
computed. Some of these small planets are the satellites of 
larger planets ; that is, they always remain near the large 
planets on which they attend, so as to form with them little 
systems of their own, although such little systems are only 



Sec. ioS.] Planets. 59 

parts of the Solar System. Some satellites, however, are 
large bodies, and show us disks. The Moon itself is the 
sllite of the Earth. Its disk is large because it is near 
us, not because it is a very large body. Small planets which 
are not satellites are sometimes called asteroids ; all of 
them which are known as yet are always at a greater dis- 
tance from the Sun than that of the planet Mars, and at a less 
nice from it than that of Jupiter. More asteroids are 
discovered every year ; at the end of the year 1S73 the num- 
ber oi known asteroids was 134. 

109. The names of the principal planets, in the order of 
their distances from the Sun, are as follows : Mercury, 
Venus, the Earth, Mars, Jupiter, Saturn, Uranus, and Nep- 
tune. Of these planets the four named first, which are 
always nearer the Sun than are any of the asteroids, are 
small compared with the other four; and only one of them, 
the Earth, is known to have a satellite. The four planets 
beyond the asteroids are large, and all of them have satellites, 
Jupiter and Uranus being known to have four each, and Nep- 
tune one. Eight distinct satellites of Saturn have been dis- 
covered, and the planet is surrounded by a ring, which is now 
generally thought to be made up of swarms of little satellites. 
Some observers have suspected that Uranus and Neptune 
also have rings ; and of course additional satellites of any 
planet may be discovered hereafter. Venus, the Earth itself, 
Uranus, and Neptune have been thought by various astrono- 
mers to have satellites, in addition to those mentioned above ; 
but no such additional satellites are known to exist. 

110. What has been learned about other planets than the 
Earth relates chiefly to their movements. The fact that they 
appear to us to move about among the stars gave them, as 

Seen said (28), their name of planets, and caused men to 
watch them more closely than any other celestial objects 
except the Sun and Moon. To show how thoroughly tl 
courses in the sky have been studied, it has been correctly 
stated that we can now tell just how a tel ould be 

placed, so as to be pointing directly at Jupiter, for instance, 



60 Outlines of Astronomy. [Sec. ho. 

at any particular moment that can be named within a hundred 
years to come. 

hi. The words real and apparent are often applied to dif- 
ferent sorts of movement with so vague a meaning that the 
explanations in which they are used can scarcely be under- 
stood. Astronomers are not in the habit of using them, but 
more commonly speak of motion in right ascension and 
declination, motion in an orbit, and so on. Such express 
have an exact meaning, and so has the phrase "apparent 
place," as used by astronomers. But this exact meaning 
cannot be comprehdnded by those who are only beginning 
the study of astronomy ; and we so often find real motions 
and apparent motions mentioned in accounts of the bodies 
belonging to the Solar System that it will be worth whil 
consider what motions may properly be called real, before 
we try to understand how the planets really n, 

112. We have seen already, in considering the Sun's rota- 
tion, that there is a sense in which no motion can be known 
to be real, because there is nothing in the universe which we 
know to be fixed. But even if we had something fixed to 
reckon from, the actual motions of other objects might not 
be called their real motions. We cannot imagine any ; 
sible way in which we could be assured that any celestial 
object was fixed, so as not to move at all : but let us suppose 
that we have been made certain of the fixity of some object 
like the Earth in every thing except its movements, and I 
we have been placed upon this fixed object. Let us now take 
a pail of water, and a piece of wood weighted with enough 
lead to make it sink in water, but not enough to make it sink 
fast. If the pail is not moved, and the sinker is put into the 
water, it will have an actual movement downwards, and this 
movement would be called a real one. But suppose that 
while it is going on the pail is lifted more quickly than the 
sinker goes down. Then the sinker would really be moving 
upwards, and yet no one would be likely to say that its down- 
ward movement was not just as real as ever. It is plain, 
then, that when we call a movement real, we do not al\\ 






Sec. 112.] Planets. 6i 

mean that it really happens. In the case we have supposed, 

the sinker has two real motions, one downward, and a quicker 
one upward ; but nothing can really move two ways at once. 

113. Suppose, next, that we were not aware at first of the 

f the pail, and only found it out after a while. As 
lon^ lid not know oi it. we should think that the down- 

ward movement ol the sinker was the only movement it had. 
Now, when we learned that its actual movement was up- 
ward, we should not consider ourselves mistaken in think- 
ing that it moved downwards. We should be as sure that 
it had a real downward movement as we were before, and 
should merely say that, besides this, it had an upward move- 
ment which was quicker than the downward movement 
already known. 

114. It seems, then, that we do not always have to make 
an entire change in our notions with regard to the movement 
of a body when we learn something new about its movement, 
or even when we have been supposing it to move one way 
and find out that it is really moving the contrary way. If it 
were not for this, we should scarcely be able to learn any 
thing at all about the movements we see ; for we should be 
always changing our minds about them. But as it is, we do 
not need to have a fixed place, like that we have just sup- 
posed ourselves to have, before we can begin to study the 
movements of things around us. When we learn something 
new about the movement of any thing, we can often under- 
stand it best by keeping our old notions about the movement, 
and supposing the moving object to have another movement 
besides that which we had learned before ; so that we con- 
sider it as moving two ways, or perhaps many ways, all at 
the same time. On this supposition we can tell where its 

ment will bring it at any time just as well as we could 
g it to have only one movement. So, too, we 
can suppose that any movement which we already know- 
it is made up of as many different movements as we 
please. If a ship is sailing northwards ten miles an hour, 
if we please, that the ship sails northwards 



62 Outlines of Astronomy. [Sec. 114. 

fifteen miles an hour and southwards five miles an hour ; and 
on this supposition we can tell correctly how much farther 
north than at present the ship will be half an hour hence. 
In the same way, we might suppose a ball rolling eastwards 
to be rolling north, south, east, and west all at the same 
time ; and there might be reasons for actually making this 
supposition ; for instance, the ball might be rolled eastwards 
in the cabin of a steamer steering west, and driven towards 
the north by a wind, and towards the south by a current ; 
and the ball, under these circumstances, might on the whole 
move towards the east. Again, when a ball is struck north- 
wards and westwards at the same time, it will be likeh 
move north-west, if the blows are about equally hard. In this 
case, too, we consider it as having two movements at once ; 
and if we choose, we can consider it as having other m< 
ments besides these : a southward and a north-eastward move- 
ment, for example ; only then we must change our notions 
of the speed of its northward and westward movements. 

115. Any movement is said to be resolved into others, 
when we consider it as made up, or, according to the usual 
expression, composed of these other movements. All the 
movements which compose any movement are considered 
real, even if none of them are really made, as often happens. 
When we learn any thing new about the movement of a 
material object, and still consider the composition of that 
movement to be what we thought it before, except that a new 
movement is added to the others, we continue, of course, to 
call all these movements real. But it may also happen that 
our new knowledge makes us change our minds with regard 
to the best manner of resolving the movement of the object 
we are observing. In this case, some of the movements 
which we formerly thought real may no longer be called real 
movements. 

116. Still, astronomers have learned so much about the 
movements of the celestial objects, that they can now be 
tolerably sure of continuing to regard many of them as among 
those into which other movements must be resolved, no mat- 



Sec. 116.] Flanets. 63 

ter what may be learned hereafter about these other move- 
ments. No one can tell, for instance, what is the actual 
movement of the Moon ; but men saw long ago that it 
would be convenient to consider a direct (42) motion 
round the Earth as one of the motions into which the Moon's 
unknown motion may be resolved. It took much more time 
and thought to show the convenience of considering a direct 
motion round the Sun as another of these motions ; but this 
is now fully admitted. Whatever may be discovered here- 
after about the movements of the Moon, we may be pretty 
sure that we shall still find it convenient to consider both its 
direct movement round the Earth and its direct movement 
round the Sun as among those motions into which its actual 
motion is to be resolved. Accordingly, these two direct 
movements are commonly said to be real. 

117. Any motion, then, is real, which we have reason to 
believe to be one of those into which it will always be con- 
venient to resolve some actual motion. But what makes it 
convenient to consider motions as resolved into certain 
others ? This question is easily answered. One great ob- 
ject of studying any science is to learn rules by which we 
can tell what to expect under certain circumstances. These 
rules are. often called laws of nature ; but they do not control 
events outside of us, but only our expectations. We are 
constantly changing and simplifying these rules, so as to 
make it easier to use them ; but by so doing we alter nothing 
in the world without us. The more we learn, the wider we 
are able to make our rules, so that a few of our new rules 
will tell us more than many of those we begin with. Some- 
times we lay down a rule which is the best we can get at the 
time, but which we expect to give up sooner or later when 
we have learned more about the subject to which it applies. 
A rule of this kind is called an empirical law. It would be 
laying clown an empirical law, for instance, to say that water 
runs down hill ; and that is a useful rule until we learn that 
quic ksilver and other liquids also run down hill, that loose- 
solids do so too, that both liquids and solids drop to the 



64 Outlines of Astronomy. [Sec. 117. 

ground when they are left without support, and also that if 
water is put under quicksilver it will run up instead of down, 
so as to come to the top of the quicksilver. When we con- 
sider all these, and many other tacts like them, we see that 
our first rule is not* exactly correct, and that if we say that 
any thing will fall through a liquid or a gas of less density 
than its own, we shall have a better rule, which we shall not be 
so likely to have to give up. Rules which are likely to last, and 
which take in many cases, are called general laws. A gen- 
eral law, of course, may be replaced by another law still more 
general. Still, it may continue to be useful for some pur- 
poses ; and so may some empirical laws. It is one of the 
objects of the study of logic to show why we should regard 
some laws as empirical, and therefore not much to be de- 
pended on, while we can regard others as general, and be 
confident that they will be found correct in all We 

need not stop here to consider the reasons which warrant us 
in thinking some laws to be more trustworthy than Othi 

118. General laws cannot always be expressed as simply 

as empirical laws, so that the\ a hard to understand. 

IW.t when they arc understood, they help us much better than 
empirical laws to know what to expect, although we often 
have to consider many general laws, or many different appli- 
cations of one general law, before we can tell what will 
happen under particular circumstances. When we are con- 
sidering a movement, for instance, we have to think what it 
ought to be according to each of a number of rules, and then 
we can tell what it will be according to all of them taken at 
once. It is now plain that we shall generally find it con- 
venient to consider every movement as resolved into otl 
each of them made according to some rule ; and we thus 
have an answer to the question which led us to consider what 
we mean by laws of nature (117), so far as any laws of nature 
relate to movements. 

119. We often see a movement repeated many times ; and 
whenever this happens, we take it for granted that there must 
be a rule, or law, for that movement. We feel still more fully 




Sec. 119.] Planets. 65 

convinced that it has a law, when it takes up very nearly the 
same length of time at each repetition. The swinging of a 
pendulum is a movement of this kind ; so is the rotation of 
the Sun, or of the Earth ; and all such, movements are called 
periodic movements. The length of time -required for each 
repetition of a periodic movement is called the period of the 
movement. All kinds of changes may be periodic whether 
they are movements or not ; variable stars, for instance, may 
change their brightness periodically. When a movement 
does not seem to be periodic, we suppose, of course, that it 
goes on according to some laws of nature ; but we usually 
presume that there must be many laws, or many applications 
of one law, to be considered before the movement can be 
explained. A periodic movement, on the other hand, is 
likely to go on according to a small number of rules ; and 
even if we can find no general laws for it, we shall expect it 
go on hereafter as it has been going on while we have 
been observing it. Now this expectation, whenever we 
express it, is itself the empirical law of the periodic move- 
ment we are studying. 

120, A uniform movement is one which always goes on at 
the same speed. The simplest kind of movement which we 
can well think of is uniform movement straight onward. 
This is not commonly called a periodic movement, because 
its period may be considered to be just as long or just as 
short as we please. But if an object moves straight on, 

pnning to move at the rate of 10 miles an hour, gradually 
quickening its speed to 20 miles an hour, and then slackening 
it to 10 miles an hour again, we shall call its movement peri- 
odic, if it goes through similar changes of speed during every 
urse. In this example we may put any fig- 
ures we please instead of the 10, 20, and 50, used above. 

121. S>me movements are considered to be both periodic 
and uniform. If an object moves ten feet north-west, then ten 
feet north-east, then ten feet north-west again, and so on in a 

Ig line, always at the same speed, it has a uniform move- 
ment, divided into parts like each other, each part being made 

5 



66 Outlines of Astronomy. [Sec. 122. 

in a given period. So, too, if any thing travels round and 
round in a ring, always at the same speed, its movement is 
both periodic and uniform. 

122. When we wish to understand any movement which 
seems to be complicated, we generally begin by trying to 
resolve it into a set of periodic movements, and, if possible, 
of uniform periodic movements, each explained by general 
laws, or at least expressed by an empirical law. The science 
of astronomy began with attempts to resolve the observed 
movements of the Sun, Moon, and planets into uniform 
periodic movements. In this way certain empirical 1 
were formed; but as empirical laws never satisfy us very 
well, the early philosophers also made guesses about the 
general laws which account for the movements of celestial 
objects; and as men still had much to learn by observation 
before any such general laws could be drawn up, their 

were often absurd. So are many of the guesses which people 
make in our own times, when they try to settle questions by 
general laws before enough has been observed to make it ; 
sible to draw Up any laws but empirical ones. We are not 
so much wiser than the early astronomers were that we can 
afford to find much fault with them for their mistakes (17). 

123. However, we are now able to explain many of the 
movements of celestial objects by certain general laws, 
known as the laws of motion. These laws can hardly be 
understood distinctly or used with success by any persons not 
thoroughly acquainted with mathematics. For the present 
we will content ourselves with an account of those motions 
of the Earth and similar objects which are considered to be 
real motions, in the sense above given to that phrase (1 17). 
Every real movement of the Earth answers to some move- 
ment' of other bodies called an apparent movement. . 
parent movements, in astronomy, are those which we should 
suppose various celestial bodies to have if we did not believe 
the Earth to have certain movements of its own. To illus- 
trate this, we will consider how it came to be believed that 
the Earth turns daily upon an axis. 




Sec. 124.] Planets. 67 

124. Nearly every one who lives either in the torrid zone 
of the Earth, or in one of its temperate zones, begins his 
acquaintance with astronomy by learning that the Sun rises 
every day On one side of any particular hill or building, and 
s on the Other ; the side on which it rises being called the 
►tern, that on which it sets the western side. It is difficult 
not to learn as much of astronomy as this ; but some people, 
perhaps, stop here, and never exactly know, when they see 
the Moon in the west soon after sunset, whether it rose there 
or not. But it takes very little observation to show that not 
only the Moon, but every star near which it ever seems to 
be, rises in the east and sets in the west, like the Sun ; and 
also that, on the whole, these stars set about as long after 
thev have risen as the Sun sets after it rises. This is 
not true of many of the other stars, however ; for if 
we are anywhere in the north temperate zone, for instance, 
and look northwards on any clear night, we shall see many 
stars which never rise or set, and some which hardly seem to 
change their places in the sky at all. One of these is the 
star of the second magnitude (81) called the North Star, and 
also Polaris (38). The bright stars apparently near it seem 
to move round it in rings, going over it from east to west and 
under it from west to east ; but even if we watch all night 
we shall not see any star go entirely round the North Star, 
because that requires about as much time as there is between 
one sunset and the next, so that the stars travel over part of 
their courses by day, when they cannot usually be seen. By 
observing stars which seem farther from the North Star than 

c we have just mentioned, we shall soon learn that they 

» go round it once in a whole day, but that the rings they 

move in are so hr^e that they care partly out of sight, behind 

the part of the Earth which lies north of us. Suppose we 

that one of the stars which seem only a little farther 

from the North Star than the North Star is from the horizon 

•ly in the evening. If it moves in a ring while it 

It, it ought to rise before morning as far east of 

north as it sets vest of north ; and so in fact it will. By 



68 Outlines of Astronomy. [Sec. 124. 

comparing its movements with those of other stars seemingly 
somewhat farther from the North Star, we can make out that 
these other stars also move in ring-shaped courses, each star 
travelling over its whole course in about a whole day ; and by 
continuing these observations, we can show that this is true 
of all the stars. We can also make out that a straight line 
drawn from some place in that part of the sky where we see 
the North Star to the place where we are, and beyond that, 
through the Earth, would pass through the middle of every 
one of the rings which form the daily courses of the st 
We shall conclude, then, that all the stars have a daily ret- 
rograde motion round the Earth, or, to Speak more exactly, 
round the line we have just described. The motion is retro- 
grade, because when we are facing north it is from right to 
left above and from left to right below ; and when we are 
facing south it is from left to right above. This retrograde 
movement can be perceived most easily at places far from the 
equator; but observations which will show that it takes place 
may be made anywhere on the Earth without much difficulty. 
125. The conclusion we have reached is an empirical law, 
and a true one ; that is, it helps us to tell beforehand, without 
making any great mistake, what we are to see in the sky at 
particular times. Accordingly, this law is still in common 
use, among astronomers as well as among other people. For 
some purposes it is convenient to regard the Sun as bavin 
daily retrograde movement round the Earth, and to consider 
this as one of the movements into which the actual motion 
of the Sun, whatever it may be. is to be resolved. If men 
had been content with statements like this, until they had 
collected observations enough of the facts of nature to enable 
them to lay down correct general laws about the daily move- 
ments of the stars, their astronomical knowledge would have 
been sound as far as it went. They need not have kept 
themselves from guessing at these general laws ; for it is 
usually necessary to try a number of guesses before any gen- 
eral law can be found. But then the guesses ought to be of 
a kind that can be tried by observation ; if we guess to save 




Sec. 125.] Planets. 69 

ourselves the trouble of observing, instead of to give our- 
selves some particular thing to observe, we shall make no 
progress in kndwle 

ss ictually made at the general law of the 
daily periodic movement of the stars was as follows : that 
the re fixed in a sort of shell which enclosed the 

Earth, and that this shell turned round, carrying the stars 
with it, although it could not be seen, because it was trans- 
parent. Now if this law were true, it would still apply to 
few other movements besides those of the stars, so that it 
would be of little more service than the empirical law instead 
of winch it was meant to be used. Besides this fault, the 
guess had another, that it did little to help on the observa- 
tion of natural facts, and mainly served to make people think 
they knew something more than they did. It was taken by 
many men for a piece of knowledge, instead of a guess ; so 
that, so far as it had any effect on the study of astronomy, it 
rather hindered than helped it. 

1:7. Another ancient explanation of the daily movements 
of the celestial objects was that which we now consider to be 
correct. This explanation is that the Earth has a direct 
movement of rotation about an axis, and that one whole day 
is the period of this movement. This periodic movement is 
only one of those into which we resolve so much of the 
actual motion of the Earth as we have yet discovered ; and it 
is to be regarded as a real movement in the sense above 
given to that phrase, but not as a movement actually per- 
formed, for two reasons. First, we do not know, and proba- 
bly never shall know, what the actual motion of the Earth is ; 
and secondly, if we suppose that we have already discovered 
the whole of this actual motion, then the actual course of any 
part of the Earth is not round and round, but onward in a 
peculiar winding curve ; so that if we could have a clear 
notion of this movement given us, we should scarcely think 
it a periodic movement, or a movement made according to 
any laws simple enough to be found out. On the other hand, 
if we could be made certain that each part of the Earth al- 



yo Outlines of Astronomy. [Sec. 127. 

ways fronts the same way, so to speak, our belief in the 
Earth's real movement of rotation would not be altered, un- 
less our present laws of motion were given up. We should 
simply have to suppose the whole universe, including the 
Earth, to have a daily retrograde rotation, just quick enough 
to counteract the direct rotation of the Earth. But, so far as 
we know, we cannot be made certain of any thing about the 
movements of objects, except that we can learn how they 
move with respect to each other. We may be sure, for 
instance, that two objects are coming nearer to each other, 
or going farther apart; but if they are coming together, we 
cannot tell whether this is because each is moving towards 
the other, or because one is stationary and the other moving 
towards it, or because both are moving the same way, but 
one taster than the other. We may resolve their movement 
towards each other into movements of as many kinds as we 
please, and we may suppose either of them stationary, when- 
ever we find it convenient; but the use of all this is not to 
decide how the two objects actually move, but to help us to 
know how far apart they will be at any time hereafter. Th.it 
is, we want to know what to expect ; and for this purpose we 
resolve movements into others, and draw up the simplest and 
most general rules or laws of nature which we can invent. If 
any one could make a set of laws of motion by which we could 
foretell, more correctly and more easily than by the laws of 
motion now accepted, the results of the various movements 
going on upon the Earth and in other parts of the universe, 
these new laws would take the place of the old ones. But it 
is useless for people to propose new explanations of the 
movements of the planets, or to find fault with the explana- 
tions now in use, unless they show us some new way of cal- 
culating the results of all movements, whether those of the 
planets or any others, and also show by examples enough 
that this new way is easier to use than the old one, and that 
its conclusions agree with the facts of nature. Now, if we 
can be sure of any thing in human affairs, we may be sure 
that laws of motion which have been tried for centuries and 



Sec. 127.] Planets. 71 

found always serviceable cannot he set aside by new discov- 
eries, although perhaps some law may be found by which 

eral of them may be all stated at once. Accordingly, 
there is not the least reason to expect that the movements 
we now call real movements will not continue to be called 
so ; and any one who fancies he has made some new discov- 
erv about them must satisfy us that he knows accurately what 
astronomers think about them now before we can pay the 
least attention to his theories. 

12S. When the rotation of the Earth was first proposed as 
an explanation of the daily movements of the stars, hardly 
any general laws of motion had been discovered. It was 
known, however, that small solid objects are more likely than 
large ones to move about with respect to each other and to 
the objects around them. Great rocks and hills do 

not move about over the Earth like the pebbles tossed up by 
the sea or the thistledown floating in the air. This, after all, 
is only an empirical law, and is not entirely accurate. So 
far as it is true, it follows from the general laws of motion 
now known. At first, this empirical law seemed to be against 
the supposition of the Earth's rotation, because the distance 
of the stars was not known, and it was thought that they 
might be small objects compared with the Earth. Still, the 
guess that the Earth rotates was better than the guess that 
the stars are fastened to a rotating transparent shell (or 
crystal sphere, as it was called), because it would naturally 
set people to observing the Earth and to trying to make out 
the distance of the stars ; whereas there was little to be ob- 
served about an imaginary transparent object. But in fact, 
the astronomers who first guessed at the rotation of the Earth 

not seem to have been diligent observers, compared with 
some other astronomers of their times. By degrees, astron- 
omers learned to determine the distance of the Moon toler- 
ably well, and it became obvious that the other celestial 

were farther off than the Moon. As knowledge 
this kind increased, it became more and more reasonable to 
suppose that the Earth might be only a small object com- 



72 Outlines of Astronomy. [Sec. 128. 

pared with others in the universe ; so that the law which had 
formerly seemed to be against the supposition that the Earth 
rotates came to be rather in favor of it than otherwise. Other 
facts were gradually discovered, all showing that it would be 
necessary to consider the Earth as a rotating body in order 
to explain the facts of movement among celestial objects in 
the same way in which terrestrial movements were explained. 
Finally, but not till long after the opinion that the Earth 
rotates had been generally adopted, experiments were con- 
trived which show that we must consider the Earth to rotate, 
or else give up the most general laws of motion vet discovered. 
One of these experiments consists in watching the swinging 
of a weight hung up by a cord or wire : but although this 
seems very easily done, the experiment needs much care to 
make it succeed, for the following reason. 

129. If a weight is hung up and left until it seems to 
remain perfectly still, and then drawn to one side and let 
it will probably not swing back exactly to the place from 
which it was moved, which we will call its place of rest, but 
will pass a little to one side of it or to the other. After 
Swinging some distance beyond this place the weight will of 
course swing back again, passing its place of rest on the side 
opposite that on which it went in its forward swing. It will 
continue to swing round this place, instead of through it, as 
long as it goes on swinging at all. Now, according to the 
laws of motion, it cannot do this and yet keep on following 
the same track with respect to the objects around it which it 
followed the first time it swung forward and back. Let us 
suppose that it was drawn towards the north from its place 
of rest, so that it began swinging nearly north and south ; 
and let us also suppose that when it first swung southwards 
it went a little east of its place of rest. Then, when it is 
about to begin to swing northwards again, it will be a little 
farther west than it would have been if it had gone straight 
through its place of rest instead of going east of it. When 
it is about to swing southwards for the second time, it will 
be a little east of the place from which it set out the first 



Sec. 129.] Planets. 73 

time. If we suppose it to have begun by passing to the west 
instead of to the east of its place of rest, it will shift its 
course the other way. On either of these suppositions, if it 
kee] aging long enough, it will after a time be swing- 

instead ot north and south ; and if it was 
hed to one side when it was first let go, so as to swing 
siderably west or east of its place of rest, the shifting of 
its course will be quick enough to be noticed every time it 
swings. 

130. This experiment is easy to try, although it may some- 
times be interfered with by disturbances in the air of the 
place or the framework of the building where it is tried, or 
by some resistance in the fastenings of the cord or wire 
which holds up the weight. But although it is in itself an 
interesting experiment, it gives us no distinct information 
about the rotation of the Earth. If, however, we can succeed 
in setting the weight in motion with so little disturbance that 
it goes at every swing straight through its place of rest, then 
also its course will shift, but more slowly than before, and 
in a way which depends en the part of the Earth where the 
experiment is tried. To understand the reason for this, let us 
first suppose that the experiment is tried at one of the Earth^s 
poles. As the weight swings farther and farther away from 
the pole, it passes over ground which is moving more and 
mure quickly by reason of the Earth's rotation. The weight, 
accordingly, falls a little behind the ground over which it 
moves, somewhat as a boat which has been rowed across a 
river to a place exactly opposite that from which it started is 
farther up stream than a floating lo^ which was just in the line 
of its course when it set out. To complete the comparison, 
>ose the current to crow swifter as the boat pjoes 
on. When the weight swings back past the pole, it begins to 
pass over ground which is moving the other way from the 
ground over which it swunij just before. This series of 
changes will be repeated every time the weight swings, and 
the course of the weight will therefore shift a little every time 
with respect to the ground beneath it. If the resistance of 



74 Outlines of Astronomy. [Sec. 130. 

the air and the stiffness of the apparatus did not give the 
weight some additional movement beyond that of swinging, 
its course would shift just as fast as the Earth rotated ; so 
that at the end of one complete rotation of the Earth, the 
weight would be swinging just as it was at first; while at 
the end of half a rotation, the only difference would be that 
the forward swing of the weight would carry it over the 
ground the same way that its backward swing took it at 
first. 

131. If the experiment is tried elsewhere than at one of 
the Earth's poles, the weight will not shift its course so 
quickly as in the case just supposed. At the equator, in- 
deed', the Earth's rotation will have no effect on the motion 
of the weight, and the effect increases, according to known 
laws, with the latitude of the place where the experiment is 
tried, increasing, however, more rapidly while the latitude is 
small than when it is considerable. The effect is stated in 
mathematical language to be proportional to the sine of the 
latitude. 

132. A heavy weight hung by a long wire is lust adapted 
to the purpose of this experiment, which has sometimes I 
tried on a great scale in lofty buildings. However it is tried, 
the weight, when drawn aside at the beginning of the experi- 
ment, must be held back by a wire loop passed loosely round 
it, the loop being attached to some support by means of a 
combustible cord. When the weight has become entirely 
quiet in its new position, this cord is burned off by the flame 
of a match or candle held beneath it ; the loop then drops off 
the weight, which begins swinging without any movement 
sideways, if the experiment has thus far been successfully 
performed. When it is tried on a small scale, pains must 1 e 
taken to have the support firm, the weight smooth and round, 
and the air around it quiet. If the observer closes one eye 
and rests his head against some steady support, he can tell, 
by looking along the course of the weight at the string or 
wire on which it hangs, whether it is swinging straight or 
not. If it is, the string or wire will seem to keep the same 



Sec. 132.] Planets. 75 

place, during the movement of the weight, upon whatever 
background may he beyond it ; the flame of a steadily burn- 
ing lamp, or a well lighted screen, with distinct marks upon 
it, will answer for- tins background. If any swaying move- 
ment can be seen, the experiment has failed. But after the 
weight has swung a few times without swaying, the observer, 
if he is in the northern hemisphere of the Earth, will have to 
shift his head slightly towards the left to keep his eye in the 
line of the movement. If he is in the southern hemisphere, 
he will have to move his head towards the right ; the apparent 
shifting of the weight's course being everywhere retrograde, 
since the rotation of the Earth is a direct movement. Even 
when the experiment is carefully tried, the weight will probably 
soon begin to sway a little ; but before this happens, it may 
have had time to show distinctly which way its course was 
shifting under the effect upon it of the Earth's rotation. The 
experiment will sometimes succeed with simple apparatus, 
such as a hollow india-rubber ball filled with shot and hung 
by a piece of floss silk some six or seven feet long, one end 
of it being carefully let into the ball, and the other, by means 
of a little plaster, into the ceiling. 

133. The instrument called the gyroscope may also be 
used to illustrate the rotation of the Earth. It consists of 
a round flat piece of metal, with a heavy rim, set in such a 
frame that it can balance itself in any position. When it 
is made to spin round rapidly, it changes its position with 

to the objects around it in a manner which may be 
accounted for by the Earth's rotation. 

134. Experiments of this kind show us the exact difference 

I and apparent motion. When a swinging weight 

shi: v ' rhich it swings, the only fact we can 

is that the weight and the Earth have changed place 

in a certain way with respect to each other. What the actual 

• movement of either has been we do not pretend to know ; we 

cannot that neither of them has moved, but we can 

• of them to be stationary, and try to explain 

the movement of the other with respect to it by general rules 



76 Outlines of Astronomy. [Sec. 134. 

of some kind. The empirical law that small bodies move 
more than great ones would lead us to suppose the Earth 
stationary, and to resolve the observed movement entirely into 
movements made by the swinging weight. But the general 
laws of motion, which afford us by far the most convenient 
and exact methods of explaining the observed movement, 
require us to consider it as due to a real swinging movement 
of the weight and a real turning movement of the Earth ; so 
that one of the movements which we are at first inclined to 
attribute to the weight is not to be regarded as real. In 
other words, the shifting of the course along which the 
weight swings is only an apparent movement, due to a 
Change of place on the part of the observer, who is carried 
along with the Earth in its rotation. 

135. In most cases of movement observed by astronomers, 
as in the instance just given, the laws of motion do not allow 
us constantly to consider any one of the observed objects 
motionless. Still, we must have something fixed before we 
can determine the period of a periodic motion. We 1, 
already noticed this difficulty when we were considering the 
period of rotation of the Sun (43), and we are now ready to 
try to remove it. A meridian of the Sun, like a terrestrial 
meridian, is a line drawn round it as directly as may be, and 
passing through both poles. Now if we consider neither the 
Earth nor the Sun as having any other movement than that 
of rotation, then the period of the Sun's rotation will be that 
during which every meridian we choose to suppose drawn 
round the Sun has been twice turned edgewise towards any 
particular place in the Earth's axis. But, in fact, we consider 
the Earth and Sun as having other movements besides their 
rotation, and we can calculate their change of place with re- 
spect to each other, so far as it depends on these movements, 
from any one particular moment to any other. Supposing, 
then, these movements not to take place during one rotation- 
of the Sun, we can calculate how much difference there is 
between the rotation of the Sun as it would be observed 
under such circumstances and as it is actually observed. 



Sec. 135.] Planets. 77 

Taking this difference from the actually observed period of 
the Sun's rotation with respect to the Earth, we have the 
period which one rotation of the Sun is considered to occupy. 
Any new movements of the Earth and Sun which may be 
discovered, such as the exact movement of the Solar System 
in the universe, may cause us to alter what we call the period 
of the Sun's rotation : but, in fact, the only movements of 
importance in this inquiry are those by which the Earth is 
yearly carried round the Sun ; more especially while the 
present uncertainty about the nature of the movements of 
solar spots with respect to each other continues. Any cor- 
rection which may hereafter be made in the period assigned 
to the Sun's rotation will undoubtedly be very small, so far as 
it depends upon real motions of the Earth or Sun which 
are neglected by the astronomers of our times or unknown 
to them (46). 

136. We have now considered the general meaning of the 
expressions which must be used in describing the movements 
of the planets. We must next settle on some meaning for 
the words north and south, direct and retrograde, when they 
are used with regard to bodies beyond the Earth, so as to 
avoid the necessity of a separate explanation for each body, 
such as that employed above in describing the Sun (38). 

137. One of the real motions of the Earth carries it round 
the Sun once a year. Let us imagine a straight line drawn 
at some particular time through the exact middle of the axis 
of the Sun. directly towards the middle of the Earth's axis, 
and reaching both ways as far as we please from the Sun. 
The . will move away from this line at once; 
but we iv the line as remaining fixed to the Sun's 

re as carried about with the Sun in all its 

movements except th . "ion. Now suppose a number 

■ n in the same way at different times. They 

the middle of the Sun's axis as the prin- 

1 in a spider's web stretch out every way from the 

middle of the web; and we may suppose the spaces between 

i by other straight lines, as the web is filled 



78 Outlines of Astronomy. [Sec. 137. 

up by cross threads. To distinguish between these two kinds 
of lines, we will call them principal lines and cross lines. 
The principal lines all cross each other at the middle of the 
Sun's axis, but nowhere else. Now let us suppose a number 
of cross lines joining any two of the principal lines and 
reaching both ways as far as we please beyond the lines 
which they join. We have now a sort of web of lines, con- 
taining, however, only two principal lines. All these lines 
might be touched at once along the whole length of each of 
them by any thing perfectly flat and sufficiently large. This 
is expressed in mathematical language by saying that all the 
lines lie in the same plane ; what is meant by a plane being 
a perfectly flat partition or boundary, separating the universe 
into two distinct parts, but not itself taking tip any room in 
either part. If we suppose a sheet of paper laid upon a per- 
fectly flat table, and pressed so closely against it that the.point 
of a pin stuck through the paper goes immediately from the 
paper into the table, this point nevertlu 1 through the 

division, or, in other words, through the plane, which bounds 
the under side of the paper and the top of the table. If the 
table is tilted out of place, then this plane may he n 
as tilted along with it. A plane, then, may be said to roi 
or, in fact, to have any kind of movement which a material 
object can have ; because it can always be regarded 
bounding some flat material object, with which it moves 
about. 

138. Let us now suppose the plane in which lie our two 
principal lines to have a movement of rotation about oiu 
these principal lines as an axis. We will suppose that the 
other principal line takes no part in this movement, so that 
it is no longer in the plane as soon as the movement has 
begun. The cross lines, however, may be considered as 
belonging to the plane, and moving with it. Now, as a 
matter of fact, the plane will have made only a very small 
fraction of one complete rotation before any one whatever of 
the principal lines has been touched by some of the cr 
lines w r hich we may suppose to have been drawn in the plane. 



Sec. 138.] Planets. 79 

In other words, any principal line will be made to lie in the 
plane containing any two principal lines by a small movement 
of rotation o\ that plane. Still more simply, we may say that 
all the principal lines lie nearly in one plane. 

l;>5>. The plane in which lie any two principal lines may 
be called the plane of the ecliptic. For our present pur- 
poses, it makes no difference which two principal lines we 
take to determine this plane, since the results will be much 
alike in all cases. The plane of the ecliptic cuts the Sun in 
halves, and, like all planes, separates the universe into two 
distinct parts ; but these parts do not always remain the 
same, since the plane of the ecliptic is considered as fixed 
to the Sun's axis, and therefore carried about by the Sun, 
although not taking part in the Sun's rotation. The distance 
of the Earth from the nearest part of the plane of the ecliptic 
is never more than a small fraction of its distance from the 
Sun ; this appears from the manner in which the plane of the 
ecliptic has been described. But it must be observed that 
the name " plane of the ecliptic" has various meanings in 
astronomy, although these meanings do not differ much from 
each other, and can easily be distinguished by the nature of 
the reasonings in which that name is used. The sense which 
has just been given to it is a convenient one for the purpose 
of describing the movements of the planets, and when we are 
acquainted with these movements, it will become easier to learn 
new methods of defining the plane of the ecliptic. 

1 JO. The Sun's axis is not itself a line lying in the plane 
of the ecliptic : therefore, since that plane passes through its 
He, its northern half always lies on one side, called the 
northern side, and its other half on the southern side of the 
plane of the ecliptic. We have now the means of understand- 
bg what is menu l.y the direct movement of a planet round 
the Sun. S that the planet could be watched from 

the middle of the Sun l.y an observer placed on the northern 
<>f the ecliptic, and with his feet towards 
tnat If the planet goes round the Sun in such a man- 

ner that it passes in front of this observer from right to left, 



80 Outlines of Astronomy. [Sec. 140. 

then its motion is direct, according to the account of direct 
motion already given. If it goes exactly over the ol 
head and beneath his feet, its motion cannot be said to be 
either direct or retrograde, for it can never be said to pass 
in front of him from one side to the other. It may then be 
said to move in a plane perpendicular to the plane of the 
ecliptic, in which the Earth has been said to move round 
the Sun. It is very unlikely, of course, that any two bodies 
should be found to move in planes exactly perpendicular to 
each other ; but if many of the bodies belonging to the Solar 
System moved in planes nearly perpendicular to the plane of 
the ecliptic, there would be little convenience in distinguish- 
ing between those of them which had direct and those which 
had retrograde motion. But in fact th< rery few such 

bodies, and none of the principal plain dis- 

tance from the plane of the ecliptic which is considerable 
when compared with their distance from the Sun. 

141. When any planet which has an axis of rotation is on 
the northern side of the pi. me of the ecliptic, its northern 
pole is the pole farthest from that plane ; when it is on the 
southern side of the plane of the ecliptic the same northern 
pole is of course the nearer of the two to that plane. 

142. Every known planet has a real direct movement 
round the Sun ; every planet known to have any rotation upon 
an axis has direct rotation. Planets move round the Sun ac- 
cording to the laws o\ motion already mentioned. It follows 
from these laws that if we suppose lines drawn through the 
middle of the Sun's axis towards any planet at different ti: 

we shall find, as in the case of the Earth, that these lines are 
nearly in one plane, if we suppose them all carried about with 
the Sun. We can then suppose the direction of all but two of 
these lines slightly altered, so as to make them all lie exactly 
in the same plane with those two lines, and call this plane the 
plane of the planet's orbit. We may next suppose a ring- 
shaped line drawn round the Sun in this plane, or, in other 
words, so as to cross every straight line of this plane which 
can be drawn through the middle of the Sun's axis. This rinir- 






Sec. 142.] Planets. 81 

shaped line must have some regular geometrical form, but 
must be drawn so that the planet may never be very far from 
the nearest part of it ; it may then be called the orbit of the 
planet. Now the laws of motion will make it convenient to 
regard the movement of the planet round the Sun as resolved 
into a motion in an orbit and certain other motions. We 
may say. accordingly, that the planet has a real motion in 
its orbit, although its actual place may hardly ever exactly 
agree with any place in this orbit ; so that a planet's orbit is 
not exactly the same as its course, or path, around the Sun ; 
while neither its orbit nor its path round the Sun is the same as 
its actual course in space, of which we shall still be ignorant 
even after we have learned to attribute many real motions 
to the planets in addition to those we now r attribute to them. 

143a The plane of the Earth's orbit is the same with the 
plane of the ecliptic ; but the Earth's orbit is not the same as 
the ecliptic. The explanation of the word ecliptic belongs to 
practical astronomy, and will be given hereafter. 

144. Since the orbit of any planet, and the plane of that 
orbit, are not visible objects, like the planet, itself, but are 
only contrivances of our own, invented to help us to compre- 
hend the planet's movements, it is not surprising that astron- 
omers have found it convenient to consider orbits sometimes 
as lines having a fixed position with regard to the Sun, and 
at other times as shifting their places to some extent accord- 
to certain rules. This makes it difficult to define a plan- 
etary orbit or its plane in any way which will include all the 
meanings given to those expressions by astronomers, except 
by the aid of mathematical symbols ; and the use of these 

ur reasonings correctly, often 

distinct understanding of the whole 

subject of ti. But as the various meanings 

of a planetary orbit and its plane differ only slightly from 

ie of these meanings, such as 
that just given, will be enough to enable us to make our- 
sel % . tinted with the general results of astronomical 

rch. 

6 



82 Outlines of Astronomy. [Sec. 145. 

145. The orbits of all known planets are elliptical. An 
ellipse may be drawn by fastening a thread to two pins stuck 
into a piece of pasteboard, fur instance, and then moving a 
pencil over the pasteboard so as to keep the thread always 
stretched tight ; that is, the pencil must move so that the 
whole distance to its point from one pin and from that point 
to the other pin always remains the same. If the thread is 
not much longer than the distance between the pins, the 
ellipse will be narrow in proportion to its length ; and if 
instead of a thread we have a stiff wire stretched straight 
from one pin to the other, then the ellipse will be nothing but 
a straight line between the pins ; or, in other words, its width 
will be nothing in proportion to its length. On the other 
hand, if the pins are very close together in proportion to the 
length of the thread, the ellipse will be nearly as wide as it is 
long; and if both ends of the thread are fastened to a single 
pin, there is no longer any distinction between width and 
length in the ellipse, which is then called a circle. The 
places of the pins in the pasteboard are called the foci of the 
ellipse. The centre of the ellipse is half- way from one focus 
tc the other. The straight line from one end of the ellipse to 
the other, passing through both foci and the centre, is the 
major axis of the ellipse ; half of it is the semiaxis major. 
The quotient obtained by dividing the distance between the 
centre and either focus by the semiaxis major is the eccen- 
tricity of the ellipse ; that is, if each focus is half way from 
the centre to the end of the ellipse, the eccentricity is J. If 
the ellipse is nearly a circle, the eccentricity is nearly o ; for 
then the foci are close to the centre. If the ellipse is nearly 
a straight line, the eccentricity is nearly 1 ; for then it is 
almost as far from the centre to either focus as from the cen- 
tre to either end of the ellipse. All this will be easily under- 
stood by any one who will take the trouble to draw several 
ellipses of different shapes. 

146. In every planetary orbit the Sun is not in the centre, 
but at one focus of the ellipse. When the planet is at that 
end of the ellipse nearest to the Sun, it is at its perihelion ; 



PLATE III. 




2 inches ; o\ inches between foci ; hence eccen- 
tricity ,'. .:rcely differs in appearance from a circle. The 
eccent: than a of \. 

: ; hence eccentricity \. 
:c eccentric than that of the orb:: | '.met. 

-c ccccntric- 
Qtlic than the orbit oi 



Sec. 146.] Planets. S$ 

when it is at the opposite end it is at its aphelion. The 
itest eccentricity of any known planetary orbit is about .1 ; 

a planet having such an orbit is about twice as far 
from the Sun when it is at its aphelion as it is when it passes 
perihelion. The orbits of the larger planets are less eccen- 
tric ; the eccentricity of the Earth's orbit, for instance, is only 
about ) that the Earth's orbit is much like a circle. 

117. Since the distance of a planet from the Sun is differ- 
ent in different parts of its orbit, this distance cannot be set 
down in figures which will always be correct. Accordingly, 
when the Earth, for instance, is said to be about one hun- 
dred and eight times as far from the Sun as the poles of the 
Sun are from each other, what is meant is that the semiaxis 
major of the Earth's orbit is about one hundred and eight 
times as long as the distance between the Sun's poles. The 
length of the semiaxis major of the orbit of any planet is what 
is called the mean distance of that planet from the Sun ; 
and when a planet's distance from the Sun is mentioned, we 
understand that this mean distance is meant, unless we are 
expressly told that it is not. 

1-1S. Planets move faster in their orbits the nearer they 
are to the Sun ; so that, of a number of planets, that which 
is nearest to the Sun moves quickest, and each moves faster 
at its perihelion than at its aphelion. A straight line drawn 
from that focus of a planetary orbit at which the Sun is 
situated to that part of the orbit in which the planet is 
situated is called the radius vector of the planet ; and this 
radius vector may be supposed to be carried round with the 
planet, like an elastic string joining it to the Sun, and short- 
ening qt lengthening as the planet approaches the Sun or 
retires from it. On this supposition, the radius vector sweeps 
over the whole of the space surrounded by the orbit while the 
planet travels once over the whole circuit of the orbit ; and 
while the planet travels over any given part of that circuit, 
the radius vector sweeps over a corresponding part of the 

hich the orbit encloses. Now the rate of any plan- 
motion along its orbit is such that the space swept over 



84 Outlines of Astronomy. [Sfx. 148. 

by its radius vector in a given time is equally large in all 
parts of the orbit. This space will have different shapes in 
different parts of the orbit. Near the perihelion it will be 
comparatively short, measured from the Sun to the planet, 
and comparatively wide, measured along the orbit ; near the 
aphelion it will be comparatively long and narrow ; and in all 
cases it will of course run up to a point at that focus of the 
orbit where the Sun is situated. But it will always be equally 
extensive, or, to use a geometrical phrase, it will always have 
the same area. To make this clearer, let us suppose that the 
orbit of a planet runs along the edge of an elliptical metal 
plate of uniform thickness, so that a square foot of this plate 
taken from any part of it will weigh just as much as a square 
foot taken from any other part. Let us suppose a pin to he 
set in this plate at that focus of the ellipse which is in ; 
occupied by the Sun ; and suppose an elastic string com, 
ing the planet with this pin to represent the radius vector. 
Then the weight of that part of the plate touched by the 
string during ten days, for instance, while the planet is mov- 
ing in one part of its orbit, will be the same as the weight of 
that part touched by the string during any other ten d 
while the planet is moving in some other part of its orbit. 
That is, although these parts of the plate may be of different 
shapes, they contain equal quantities of metal. 

1-10. If one planet is tour times as far from the Sun as 
another, it will be eight times as long as that other plauet in 
completing its circuit round the Sun ; if it is nine times as 
far from the Sun, the time of its circuit will be twenty-seven 
times as great; if it is sixteen times as far from the Sun, the 
time of its circuit will be sixty-four times a .and so 

on, according to the same rule. The general statement of 
this rule is that the squares of the periodic times of any two 
planets are to each other as the cubes of their mean dis- 
tances ; but the above instances of its application may per- 
haps give a better notion of its meaning than this general 
statement does. The distances of the planets are not related 
to each other in such simple proportions as those just used 



Sec. 149.] Planets. 85 

for the sake of illustrating the rule, so that the fractions 
showing its actual use are too complicated -to allow their 
relations to be easily seen. 

1.30. The rules which have just been stated are generally 
known as Kepler's laws. Stated briefly, they are as fol- 
lows : — 

The orbit of every planet is an ellipse, at one focus of 
which the Sun is situated. 

The radius vector of every planet traverses equal spaces in 
equal times. 

The squares of the periodic times of any two planets are to 
each other as the cubes of their mean distances. 

151. The progress of astronomy since the discovery of 
these laws has enabled us to show not only that they are 
special instances of the working of the general laws of mo- 
tion, but also that they are not perfectly exact statements. 
However, what has been said about the true nature of real 
motions will make it seem likely, at least, that if Kepler's laws 
do not express the whole truth respecting the movements of 
the planets, they may still be considered accurately true 
when their language is fully understood. In fact, they still 
remain the best known summary of our knowledge upon the 
subject to which they relate ; and there is accordingly no 
reason to suppose that they will go out of use in astronomi- 
cal works. 

152. The second and third of these laws are evidently in 
some way related to each other, on the supposition that any 
general rules for the velocity with which planets move can be 
laid down. For the second law determines the relative speed 
of a planet in different parts of its orbit, while the third deter- 
mines the relative speed of different planets ; and the result 

oth cases depends upon the distances from the Sun of 
the planets which are considered. But at first sight these 
n inconsistent with each other. If we try 
to extend the application of Kepler's second law to the move- 
ments of separate planets, we shall expect to find the move- 
ment of a planet four times farther from the Sun than another 



86 Outlines of Astronomy. [Sec. 152. 

not eight but sixteen times as slow as that of this other 
planet. But the laws of motion must be separately applied 

to the case of each planet, when we wish to determine its 
movements. We cannot take it for granted that all planets 
move alike, although we may take it for granted that there is 
little change from time to time in the rules by which the 
movements of any one planet are to be calculated. Kepler's 
second law applies to many movements besides those of 
celestial objects. Let a small weight, for example, be whirled 
round a few times at the end of a string, and let the string be 
allowed to coil itself round the linger as the weight continues 
to revolve. The increase of speed in the movement of the 
weight as the string shortens will illustrate the same rule as 
that in accordance with which the Earth quickens its move- 
ment round the Sun as it approaches its perihelion. 

153* The laws of motion, as now understood, will be ex- 
plained to some extent in that part of this work which relates 
to theoretical astronomy. It will be enough for the present 
to state that the Earth or any other planet falls towards the 
Sun, according to the laws of motion, as a ball thrown into 
the air, or fired from a gun, falls towards the Earth. The 
impulse given to such a ball is counteracted by the resistance 
of the air, and at length fails any longer to keep the ball from 
coming to the ground. Even if there were no air to stop the 
ball, it might strike against the ground in some part of its 
course, and thus be prevented from circulating round the 
Earth, as the Moon does, and as the Earth itself circulates 
round the Sun. But if the ball were thrown forward horizon- 
tally with sufficient force, or if the Earth would open before 
it as it came to the ground and give it a free passage, it would 
go, in the absence of air or other impediments, not exactly 
towards, but past the middle of the Earth, round which it 
would continue to travel in an ellipse or a circle, unless its 
original speed had been too great. In that case it would 
move away from the Earth altogether in one of the curves 
known as parabolas or hyperbolas, its falling movement bein^ 
enough to bend its course a little,, but not enough to bring it 
back. 




Sec. 154.] Planets. 87 

154. The mass of the Sun being more than 320,000 times 
that of the Earth (47), we say that the Earth tails towards, or 
rather falls past, the Sun. not the Sun towards or past the 
Earth ; just as we say that a ball falls towards the Earth, not 
the Earth towards the ball. Still, in the strict application of 
the laws of motion to all facts of the kind we are now con- 
sidering, we must speak of the movements performed by each 
of at least two bodies with respect to the other ; for example, 
we must say not that the Earth falls towards the Sun, but that 
the Earth and the Sun fall towards each other, while their 
forward movements keep them from meeting anywhere, and 
these falling and advancing movements taken together make 
them circulate perpetually around each other. But the share 
of the Eartli in this joint movement is far larger than that of 
the Sun, much as a horse, when employed to move a large 
building by means of a windlass, has to travel a great deal 
farther than he carries the building. 

155. The Earth is not hindered in its forward movement 
by any thing capable of checking it as the air does a ball. 
The ether may possibly retard it a little, but is not known to 
do so. The meteors which are constantly striking the Earth 
may also check its course, but they have not yet produced 
any noticeable effect upon it. The laws of motion do not in 
themselves account for the fact that the Earth has a forward 
movement as well as a falling movement; they only show 
what will happen when this forward movement is once begun. 
There has been much speculation upon the origin of move- 
ments of this kind among the celestial bodies, but it is not 
worth while for any but accomplished astronomers to pay 
attention to so difficult a subject (17) as that of the origin of 
the present structure of the universe. Whatever knowledge 
of past acres we may obtain, it is at all events unlikely that 
we shall be able, by astronomical research, to show the matter 
now composing the material universe to have been at any time 
devoid of motion. 

15<>. In giving an account of the peculiarities of the planets 
considered separately, it will be convenient to begin with the 



88 Outlines of Astronomy. [Sec. 156. 

Earth, because we know most about it. As we have seen, it 
has an axis of rotation, turning round on that axis once in 
about a day. That pole of the. Earth nearest Greenland is 
called the north pole, and that nearest Australia the south 
pole. To travel north upon the Earth means to travel as 
directly as possible towards the north pole. To travel east 
or west means to move upon the Earth so as to keep always 
at the same distance from the north pole ; if this movement is 
direct, it is towards the east ; if retrograde, towards the west. 
East and west, then, are words with a very different kind of 
meaning from that which belongs to the words north and 
south. There is no place on the Earth east of all other 
places on it ; but if we could travel, for example, to the 
south pole of the Earth, then we could not go any farther 
southwards, unless we could leave the Earth altogether and 
travel on along the line of its axis. If we went away at all 
from the south pole without leaving the Earth, we should be 
travelling northwards ; at first starting, we could not even 
go north-east or north-west. But as soon as we had reached 
any distance from the south pole, however small that distance 
might be, we could travel east or west round the pole as I 
as we chose without ever being as far east or as tar west as 
we could go. There are other ways in which the difference 
between the words north and south and the words east and 
west may be made to appear, but we need not examine them 
at present. 

157. If we suppose the Earth's axis divided in the middle 
into a northern and a southern half, the place cf this division 
is what we will call the centre of the Earth. Suppose a 
straight line drawn from any place on the Earth through its 
centre to the opposite side ; then the two parts of this line on 
opposite sides of the Earth's centre will be nearly equal to 
each other. The height of the Earth's mountains is not 
great enough to make a noticeable difference in measure- 
ments of its thickness (1). Any straight line drawn from 
side to side of the Earth through its centre may be called 
a diameter of the Earth : either of the two equal parts of 



Sec. 157.] Planets. S9 

a diameter which are on opposite sides of the centre may be 
called a radius ; or. as is more usual in astronomy, a semi- 
diameter. Any globular body like the Earth in shape may 
be said to have a centre, and to have diameters and semi- 
diaineters or radii, whether one of the diameters is an axis 
of rotation or not. The longest of the straight lines which 
can be drawn through such a body from one side to the other 
will be one of the diameters, and the centre will of course be 
half-way from one end of this diameter to the other. 

158« An equatorial diameter of the Earth is a diameter 
with its ends in the Earth's equator ; there may be as many 
equatorial diameters as we choose to suppose. The polar 
diameter is that which reaches from pole to pole, or, in other 
words, it is the axis, unless we make no distinction between 
the axis itself and the line of the axis, which may be sup- 
posed to reach out as far as we please from the Earth. 
There can be only one polar diameter, as appears from the 
meaning of that expression. If any diameter of a globular 
body is considered as an axis, it may be called the polar 
diameter of the body, and its ends may be called poles. The 
line drawn round the body half-way between these poles may 
then be called an equator, and diameters ending in the equa- 
tor will be equatorial diameters. 

159. If every diameter of a globular body is exactly as 
long as any other diameter of the same body, the shape of 
that body is spherical, and the body itself may be called a 
sphere. The Sun. for example, or that part of it within the 
chromosphere, is spherical in form, so far as is known ; but 
cannot be measured very accurately (76). The 
Earth cannot be considered spherical, even if we disregard 
the irregularities of its shape occasioned by its mountains 
and hollows. It has the shape of what is called in geometry 
an oblate spheroid. This means that its polar diameter is 
the shortest of all its diameters, and that its equatorial diame- 
ters are the longest. If we suppose it cut into its northern 
and southern hemispheres, the shape of the section thus 
made through it will be nearly circular ; but if it is cut into 



90 Outlines of Astronomy. [Sec. 159. 

any other pair of hemispheres, the shape of the section will 
be elliptical ; and the ellipse will be most eccentric when the 
section is made along the axis. Even then, however, the 
ellipse will be much like a circle, since the polar diameter of 
the Earth is less than thirty miles shorter than an equatorial 
diameter. Certain measurements have been thought to show 
that the equatorial diameters of the Earth differ in length to 
some extent. 

160. According to the laws of motion, every thing on or 
near the Earth must seem heavier the closer it is to the 
Earth's centre. We have just seen that the poles are nearer 
to this centre than other places on the Earth are, and that 
the ends of equatorial diameters are farthest from it. Ac- 
cordingly, the weight of every terrestrial object must seem to 
increase as it is carried from the equator towards either pole. 
But this cannot be shown with an ordinary pair of scales ; 
for whatever we put into one scale will grow heavier just as 
fast as what is put into the other scale. The rate at which a 
pendulum swings, however, depends on the length and also 
on the weight of the pendulum ; not its weight compared 
with that of another pendulum of the same length, but the 
speed with which it would drop to the Earth if allowed to fall. 
It has been found, accordingly, that a pendulum which 
swings once every second when it is near the Earth's equa- 
tor will swing a little more than once every second in other 
parts of the Earth. Although a pendulum would not swing 
much faster even at one of the poles than at the equator, 
there is still difference enough between the rates at which a 
pendulum swings in two places like New York and Panama, 
for instance, to be discovered by counting the number of 
times the pendulum swings in a few hours at each place. 
The experiment has been tried in many places and at differ- 
ent times, with all proper precautions to prevent changes of 
temperature and atmospheric resistance from affecting the 
result. It has thus been found that the difference in the rate 
of a pendulum in different parts of the Earth is too great to 
be accounted for only by the shape of the Earth, as deter- 



Sec. 160.] Planets. 91 

mined by what is called surveying. We must look, then, for 
BOme additional reason why bodies on the Earth should grow 
lighter as they are carried towards the equator. This reason 
is the Earth's rotation on its axis, which daily carries a body 
placed at the equator as far as it is round the Earth, or nearly 
25.000 miles, while a body near either of the poles is moved 
by the Earth's rotation only a short distance in the same 
time. When a carriage is driven fast over wet ground, 
the wheels take up mud and fling much of it off again every 
time they go round. This, of course, is because the lower 
part of each wheel is carried backward by its rotation, so 
that it is not moving forward as fast as the body of the car- 
riage. The top of the wheel, on the contrary, is moving for- 
ward faster than the body of the carriage. As the forward 
movement of any part of the wheel's rim grows quicker while 
that part of the rim is rising from the ground, some of the 
mud which stuck to it while it was moving forward more 
slowly is thrown off, a part at a time ; and all of it may be 
thrown off if the carriage moves fast enough. We can imag- 
ine the Earth to rotate so rapidly that any thing brought near 
its equator would in like manner be flung off, although objects 
might still rest upon it near the poles. In this case, nothing 
at the equator could be said to have any weight. We actually 
find that any object — a pendulum, for example — clings less 
firmly to the Earth the nearer we bring it to the equator, on 
account of the Earth's rotation as well as on account of its 
shape. We must remember, however, that there is a differ- 
ence between the reasons why mud sticks to a wheel and 
why movable terrestrial objects remain upon the Earth. The 
explanation of this difference belongs to mechanics rather 
than to astronomy, and does not affect the fact that material 
objects which cling together in either way mentioned above 
may be separated by a particular sort of motion. 

l(»l. It may be asked why the Earth's motion in its orbit 
does Dot lessen the weight of terrestrial objects as its rotation 
does. In the illustration just given, it is the forward motion 
of the wheel, as well as its rotation, which throws off the 



92 Outlines of Astronomy. [Sec. i6r. 

mud. But both these movements make a difference in the 
speed of the rim of the wheel with respect to the Earth. 
Now the Earth's rotation likewise makes a difference in the 
speed of different parts of the Earth with respect to each 
other ; but the Earth's movement in its orbit has no such 
effect. 

162. A pendulum, as we have now seen, may be used in 
two different ways to show that the general laws of motion 
require us to attribute a real movement of rotation to the 
Earth. The first way is to set it swinging so that it may 
shift the line along which it swings with respect to surround- 
ing terrestrial objects ; the second way is to count the vibra- 
tions it makes in a given time in different places. In this 
second method, however, the Earth's rotation is not shown 
to be direct, and the shape of the Earth has to be taken into 
account. But this shape itself, or rather the shape of the 
water forming the ocean, ~equires us, if it is to be explained 
in accordance with the laws of motion, to assume that the 
Earth rotates. The ocean extends at the equator more than 
twenty-six miles farther from the Earth's centre than it does 
near the poles. But water always settles into hollow places 
upon the Earth when it can ; that is, it flows towards the 
Earth's centre whenever matter heavier than itself does not 
keep it from doing so. The water near the equator, then, 
must be lighter, in a certain sense, than the water near the 
poles, or it would flow towards the poles and distribute itself 
over the polar regions of the Earth in such a way that the 
ocean, wherever it was situated, would extend equally far in 
all its parts from the Earth's centre. If a fluid sphere is 
made to rotate upon an axis, it takes the shape of an oblate 
spheroid, and finally, if the rotation is quick enough, it is 
changed into a ring. This experiment has been tried with 
a small quantity of oil placed in a mixture of alcohol and water 
just as dense as the oil itself. Under these circumstances the 
oil takes the form of a sphere, which may be made to rotate 
by piercing it with a wire and gently turning the wire. The 
equatorial portions of the sphere, or those which are already 






Sec. 162.] Planets. 93 

farthest from the wire, are then carried out still farther ; along 
the wire, on the other hand, the sphere contracts. If the 
Earth, according to the ordinary belief, was formerly altogether 
liquid or gaseous; we can readily account for its present form 
b) the tact of its rotation. But it is now partly composed of 
water, and this water is constantly wearing away and build- 
ing up the land, so as to distribute it in new ways. Hence 
the Earth would even now be likely to work itself gradually 
into its actual form, if it had not already been moulded into 
that form ; and volcanic action, or whatever else may tend 
slightly to alter its present shape, is counteracted by the 
waves and currents of the ocean. 

163. The trade-winds, as they are called, and in fact all the 
various currents of air and water which are observed upon 
the Earth, depend to a great extent upon the fact of the 
Earth's rotation ; but their description belongs rather to the 
study of physical geography than to that of astronomy. 

164. What has been said above of the difference in weight 
of bodies placed in different parts of the Earth may be diffi- 
cult to understand, unless some notice is taken of the vague 
meaning which the word weight commonly has. For this 
reason, the word mass (10) is always used in speaking accu- 
rately of what is sometimes understood by weight. Any 
particular piece of iron has the same mass in one place on 
the Earth that it has in another ; but, owing to the Earth's 
rotation and shape, it clings less firmly to the Earth, or, in 
one sense, has less weight, the nearer it is brought to the 
equator. 

165. The Earth has other real motions besides those already 

red. In speaking of its rotation alone, we regard its 
axis as motionless ; but we find that its various parts move 
with respect to each other in other ways than those which 
are described by saying that it rotates on its axis. To under- 
stand these movements, we must regard the Earth's centre 
only as fixed, and suppose it to swing round this ( entr 
that jts axis may be made to point to different parts of the 
universe at different times, always passing, however, through 



94 Outlines of Astronomy. [Sec. 165. 

the same parts of the Earth. To see what this motion is, we 
need something which we can consider fixed for the time of 
our inquiry, and with which the position of the Earth's axis 
can be compared. We can accomplish this in the following 
way. 

166. Let us suppose the Earth's centre to be situated in 
the plane of the ecliptic, as it will sometimes be, however we 
define that plane. Then, as a matter of fact, the hemisphere 
of the Earth lying on the northern side of the plane of the 
ecliptic will not be exactly the same as what we call its north- 
ern hemisphere, when we consider it as divided at the equator. 
Its north pole, indeed, will be on the northern side of the 
plane of the ecliptic, and its south pole on' the southern side 
of that plane. But half of its equator will be on the northern 
side, and half on the southern side of the plane of the ecliptic* 
Hence one of its equatorial diameters will he in the plane of 
the ecliptic, its ends marking the places where the equator 
passes through that plane. It the Earth should turn about 
this diameter as an axis, its equator might be made to lie in 
the plane of the ecliptic, so that the whole of its northern 
hemisphere should lie on the northern side of the plane of 
the ecliptic. To accomplish this, it would have to turn 
through about ^ of a complete rotation. The Earth has 
a real motion of this kind; but it is slow, and its amount 
never becomes large enough to be perceptible, except by 
delicate observations ; for it is reversed at regular intervals ; 
that is, the Earth tilts so as to carry its equator alternately 
a little towards and a little from the plane of the ecliptic. 
This real motion of the Earth may be called its nutation in 
latitude. But another circumstance occasions a greater effect 
of the same kind. We have seen that however we define the 
plane of the ecliptic, we shall not always find the Earth's 
centre in that plane. That is, if we determine the plane of 
the ecliptic at different times by our former method (139), 
we shall obtain a number of planes, differing from each other 
perceptibly, though not greatly. Now astronomers have 
found it convenient, under these circumstances, to consider 



Sec. i 66.] Planets. 95 

the plane of the ecliptic as gradually passing, according to 
certain rules, from one position to another. Accordingly, 
what they call the plane of the ecliptic depends upon the 
time of the events which they are considering. Changes 
of this kind must keep the Earth's equator and the plane 
of the ecliptic, as well at times when the Earth's centre is 
in that plane as at other times, from always sloping towards 
each other in exactly the same way. But the motion of the 
plane of the ecliptic is very slow, and, like nutation in latitude, 
it is reversed in the course of time ; and consequently the 
amount by which the Earth must turn to bring its northern 
hemisphere wholly to the northern side of the plane of the 
ecliptic (when its centre is in that plane) never differs much 
from fa of a whole rotation. The usual statement of this fact 
is that the obliquity of the ecliptic is about 23.1 degrees. 
Exactly fa of a whole rotation is 24 degrees, so that fa of 
a whole rotation would be more than enough to bring the 
whole of the northern hemisphere to the northern side of 
the plane of the ecliptic in the manner just described ; but as 
the amount of rotation which would be required is constantly 
changing, no figures will express it exactly, except for some 
particular moment of time. By its nutation in latitude the 
Earth tilts once back and forward in less than twenty years ; 
the tilting of the plane of the ecliptic occupies thousands of 
years at a time ; but although it goes on so long without 
reversal, and is in fact a much larger movement than nutation 
in latitude, it is so small that careful observations are needed 
to detect its results. It may be surprising to find that one of 
the movements called real is a movement of an imaginary 
thing, known as the plane of the ecliptic ; but of course the 
moving body is in fact the Earth, according to the explana- 
tions already given. 

167. We now come to more obvious real movements of the 

rth, known as precession and nutation in longitude. In 

Studying geography, we learn the places of certain circles 

which arc considered as the boundaries of the temperate 

zones, and called the Tropics and the Arctic and Antarctic 



96 Outlines of Astronomy. [Sec. 167. 

Circles. These boundaries are not absolutely fixed, but 
must be considered as changing their places according to the 
changes which we consider as taking place in the plane of 
the ecliptic ; so that wherever the Earth is, either the Arctic 
or Antarctic Circle must pass through that place on the 
Earth which is farthest from the plane of the ecliptic. If 
the Earth is on the southern side of that plane, it will be the 
Antarctic Circle which passes through this farthest place ; if 
on the northern side, it will be the Arctic Circle. If the 
Earth's centre is in the plane of the ecliptic, there will be 
two places on it farther from that plane than any others, the 
Arctic Circle passing through one and the Antarctic Circle 
through the other, fn order to have a name for these 
places, let us call them the terrestrial poles of the ecliptic. 
Wherever the Earth is, one of them at least is as far from the 
plane of the ecliptic as any terrestrial place that can be 
found ; and the other is directly opposite to it. The rotation 
of the Earth on its axis prevents these terrestrial poles of the 
ecliptic from remaining any length of time, however short, at 
any particular parts of the Arctic and Antarctic Circles. Still, 
at any moment, the Earth is to be regarded as having .1 retro- 
grade rotation, so slow that it is repeated less than four times 
in a hundred thousand years, about an axis which we may 
call the same as the line drawn from one terrestrial pole of the 
ecliptic to the other. The general name of precession is 
applied to the visible effects produced by this slow rotation, 
which may itself be called the precessional movement of the 
Earth. Considerable changes are always going on in the 
precessional movement of any part of the Earth at a distance 
from its ordinary axis of rotation, since the axis of the pre- 
cessional movement is constantly shifting. Nutation in lon- 
gitude is a smaller movement, by which precession is at.pne 
time increased and at another diminished. Precession, nuta- 
tion in longitude, and nutation in latitude (166), may all be 
considered parts of a single movement ; but it is often con- 
venient to regard that movement as resolved into others, in 
the way just described. 



Sec. 16S.] Planets. 97 

16S. In consequence of precession, the appearance of the 

sky, as seen from any particular part of the Earth, is always 

[though the change is so slow that it may go on 

lor a century at a time without being noticed by any one who 

s not make careful observations of the stars. In a thou- 
rs. however, the change would become great enough 
to be verv obvious to people who could remember the begin- 
ning and witness the end of such a period. About four thou- 
sand years ago. an observer stationed at the north pole of 
the Earth would have had a certain star (a Draconis) in the 
constellation Draco, instead of our present North Star, nearly 
over his head ; while twelve thousand years hence, the line 
of the Earth's axis will point nearly enough to Vega to allow 
that to be considered the North Star in its turn. It is well 

notice that this change is not due to any shifting of the 
place of the Earth's axis in the Earth, but to a movement of 
the Earth itself about its centre, as has been said already 

;). This movement, of course, does not change the situ- 
ation of one star with respect to another, as seen from the 
Earth, but only alters our view of the whole visible universe 
at once. 

169. Astronomers not only consider the plane of the eclip- 
tic as variable, but regard the Earth's orbit as changing in 
that plane. The most important change of this kind is a 
direct movement of the whole orbit round the Sun. This 
movement, called the revolution of the apsides, is very slow. 

170. We have now considered all the more important 
movements of the Earth. The small movements by which it 
may be considered as carried a little out of its orbit, or even 
out of the plane of the ecliptic, in spite of the supposed move- 
ments of that orbit and plane, are called perturbations, and 
depend on the places of the other bodies of the Solar System 
at particular times. 

17'- The movements of the Earth about its centre may be 
illustrated in the following manner. Take a ball of any con- 
venient size, and draw a line round the middle of it to repre- 
sent the Earth's equator. Make two dots on the ball as far 

7 



98 Outlines of Astronomy. .171. 

as possible from this equator for the poles, and mark one of 
these poles as the north pole. Stick a pin into the ball at 
this north pole, so that when the north pole is at the very top 
of the ball the pin may stand upright Take a box partly 
full of sand, level the top of the sand, and place the ball in it 
so that half of the ball may be below the top of the sand and 
half above, with the north pole in the half above the sand, 
but not at the very top of the ball. We may consider the 
level of the top of the sand as representing the plane of the 
ecliptic, its upper side being regarded as its northern one. 
If it would take about fa of a rotation of the ball, round an 
axis drawn between the places where its equator dips below 
the sand, to bring its whole equator to the level of the sand, 
and its north pole to its very top, then the ball stands with 
regard to the level Of the sand about as the Earth docs with 

regard to the plane of the ecliptic. Tut a cover partly over 

the box, so that the pin which marks the line of the .c 
point towards some place in this cover, and mark that pi 
Turn the ball round and round without moving it about in 
the sand, so as to keep the pin always pointing towards the 
marked place, and so that every part of the equator which is 
above the sand may move from the left to the right of 
tator who faces it. If the spectator £ices the north pole 
instead of the equator, the top of the ball will move from 
his right to his left. This will accordingly be direct rotation, 
and will represent the daily rotation of the Earth. Next, 
turn the ball so as to keep the north pole always just at the 
same height above the sand, and so that it may go round 
from the right to the left of a spectator facing it, but still 
without changing the place oC the ball in the sand. If the 
spectator looks directly downward on the sand, he will see 
that this movement is retrograde. This twisting movement 
will represent precession and nutation in longitude. Nutation 
in latitude may be imitated by rocking the ball in the sand, 
so that every part of its equator above the sand may remain 
above it and every part below it may remain below. If the 
same movement of the ball with regard to the sand is effected 



Sec. 171.] Planets. 99 

by holding the ball still and tilting the box of sand, the 
motion imitated is that of the change of the obliquity of the 
ecliptic ; but, as we have seen, a change in the obliquity of 
the ecliptic means only that no plane will answer perma- 
nently for the plane of the ecliptic. It may be convenient, 
instead of using sand, to place the ball on a table, over 
which a sheet of paper has been stretched at such a height 
that when the ball is set in a round hole cut for it in the 
paper, half of it will be above the paper, and half between 
the paper and the table. We must remember that these 
movements, which we imitate one by one, are only move- 
ments into which we find it convenient to resolve a part of 
the Earth's motion. 

172. The movements of the Earth except those about its 
own axis and centre cannot readily be imitated for want of 
room enough to imitate them on the proper scale. If we 
have a ball one inch only in diameter to represent the Earth, 
we need a ring over one-third of a mile across to represent 
its orbit. On the same scale, the Sun would be a ball nine 
feet through, and the Moon a little ball about a quarter of an 
inch in thickness, placed about two and a half feet from the 
ball representing the Earth. Hence all ordinary attempts to 
represent the movements of the planets tend to confuse the 
learner about as much as to help him. 

173. We need not here pay much attention to the structure 
of the Earth, with its oceans and atmosphere, for such topics 
belong I . and to physical geography. But in order 
to compare the Earth with other planets we may notice a few 
of the prevalent opinions respecting it. We know scarcely 
any thing either of its interior or of the outer portions of the 
air which surrounds it. It is generally believed that its heat 

a towards its centre ; and it has been thought that 
nner portions may be so hot as to be liquid. This, how- 
far from being proved ; and at present the opinion 
see- and that the Earth's interior is 

if not mainly in a solid state. On this theory, the 
volcanic action are explained by the heat caused 



ioo Outlines of Astronomy. [Sec. 173. 

by the rubbing together and by the crushing of portions of 
the outer parts of the Earth. These effects, again, are sup- 
posed to be caused by the gradual cooling and shrinking 
which is thought to go on in the Earth. In this way the 
outside roughnesses of the Earth, its mountain chains and 
the hollows tilled by its oceans, may be accounted for as well 
as on any other supposition. But the reasons for all ti. 
opinions cannot be understood by any but thorough students 
of mathematics and the physical sciences. 

174. As to the Earth's atmosphere, we know that its den- 
sity becomes rapidly less as it extends farther from the land 
and sea ; so that the mass of all the air more than ten miles 
from the land and sea is probably trirling compared with the 
mass of the remainder. But it is still doubtful where the 
Earth's atmosphere ends; and certain facts noticed with 
regard to Northern Lights and shooting stars have made it 
seem likely that this atmosphere reaches several hundred 
miles from the solid Earth. Some astronomers think that it 
has an actual limit somewhere, while others think it has 
none. On this view, the air is only that portion of the g 
eous matter existing throughout the universe which the Earth 
may be carrying about with it at any particular time. The 
gases existing in its outer regions may perhaps differ from 
those which have hitherto become known to chemists. 

175. The Earth, then, is an oblate spheroid (159) of 
solid and liquid matter, surrounded by a gaseous atmosphere 
of unknown extent and form, which contains much floating 
solid and liquid matter; rotating on its shortest diameter as 
an axis once in every period called a day ; revolving about 
the Sun once in every period called a year, its path in this 
revolution being nearly in a plane, called the plane of the 
ecliptic, to which its equator is inclined about 23^ degrees, 
and nearly in the shape of an ellipse of very little eccen- 
tricity ; having a peculiar twisting movement which may be 
resolved into one of precession, accomplished in over 250 
centuries, and one of nutation in longitude and latitude, 
completed in less than 20 years; at a mean distance (147) 



Sec. 175.] Tlanets. ioi 

pf about 10S diameters of the Sun from the centre of that 
body ; and known to be attended by one satellite, called the 
Moon. It will be convenient to describe this satellite before 
going on to speak of the remaining planets. In describing 
it, we must begin with an account of its movements, upon 
which our acquaintance with its other peculiarities partly 
depends. 

17G. First, then, the Moon has direct rotation upon an 
axis so situated that its equator is inclined only about i* 
degrees to the plane of the ecliptic. In other words, when 
one of the Moon's equatorial diameters lies in the plane of 
the ecliptic, which must happen whenever the Moon's centre 
comes into that plane (166), about jj^ of a whole rotation 
of the Moon about that diameter as an axis would be enough 
to bring its whole equator into the plane of the ecliptic. 
Next, the Moon revolves about the Earth with direct motion 
in an elliptical orbit. The Earth occupies one focus of this 
orbit, the plane of which is inclined about 5 degrees to the 
plane of the ecliptic. In other words, if we suppose a globe 
with the Moon's orbit for its equator, about J% of a whole 
rotation round one of its equatorial diameters as an axis 
would be enough to bring its equator into the plane of the 
ecliptic, supposing its centre to be in that plane. 

177, The time occupied by one rotation of the Moon upon 
its axis is equal to the time occupied by one of its revolutions 
about the Earth : and this time is somewhat over 27 days. 
The equality of the times of the Moon's rotation on its axis 
and revolution in its orbit keeps a large part of one half of 
the Moon always turned towards the Earth, and a large part 
of the other half always turned away from it. We may say, 
although not quite accurately, that the Moon always turns the 
same side to the Earth. Some people find a difficulty in 
understands inder these circumstances, the Moon 

tate on an axis. To get over this diffi- 
culty, it . to remember what has been said 
of real motions. If a man walks round a tree, facing north- 
wards all the time, he will be facing towards the tree when 



102 Outlines of Astronomy. [Sec. 177. 

he is south of it, and will have his back towards it when he is 
north of it. Now if we are considering his movements with 
regard to the points of the compass, we shall not resolve his 
movement into two, but consider it a single movement round 
the tree, performed without any rotation. But if we are con- 
sidering his movements with regard to the tree, we may 
resolve it into two, one movement round the tree, and one 
movement of rotation. This is what we should do if we were 
considering, for instance, the movement of a wheel placed 
with its axle north and south, and having a retrograde motion 
on that axle just equal to the Earth's direct movement of 
rotation. We should not be likely to say that such a wheel 
revolved round the Earth's axis without rotating, although we 
might if we did not consider it part of the Earth. On the other 
hand, suppose that a man walks round a tree in the ordinary 
way, with his left side, for instance, always towards the tree. 
In this case, we do not usually resolve his movement into 
two, because we consider it simply with regard to the tree. 
But if we consider it with regard to the points of the com- 
pass, we see that the man has been facing to all of them in 
turn during his circuit round the tree ; therefore his move- 
ment must be resolved into two, one of these being a move- 
ment of rotation. We do not consider a mountain on the 
Earth's equator as revolving every day round the centre of 
the Earth and also rotating on an axis of its own, but we 
might if we did not regard it as part of the Earth. The 
Moon has a similar movement, performed, as we have seen, 
once in 27 days ; and as the Moon is not part of the Earth, 
the accepted laws of motion require us to resolve this move- 
ment into one of rotation and another of revolution about the 
Earth. The need of doing so becomes very evident when we 
observe that the motion of the Moon about the Earth is not 
uniformly quick. According to the second law of Kepler 
(150) the Moon must move quickest in its orbit when it is 
at that end of its orbit nearest to the focus occupied by the 
Earth. It is then said to be in perigee; and in apogee, or 
at the opposite end of its orbit, it of course moves slowest 



Sec. 177.] Planets. 103 

But its rotation on its axis keeps on very nearly at the same 
rate, so that although the time in which the two movements 
arc completed is the same, the time in which the Moon passes 
over a quarter of its orbit ending or beginning at perigee is 
less than the time in which it completes a quarter of a rota- 
tion. On such occasions, therefore, its motion round the 
Earth outruns its rotation a little. If a man walks round 
a tree in the ordinary way, and at some part of his course 
walks quicker than before without changing front any 
quicker than before, he will begin to turn his back upon the 
tree. This answers to the movement of the Moon in perigee ; 
in apogee the opposite effect takes place ; and accordingly 
we have somewhat different views of the Moon at different 
times. But so far as our view of the Moon depends on the 
facts just noticed, we shall have the same view of it in perigee 
that we have in apogee. After passing its perigee it will first 
move comparatively fast in its orbit, but constantly slacken 
speed, so that by the time it reaches apogee, it will have lost 
as much as it has gained upon its movement of rotation. On 
passing apogee it will still lose for a time, but continually lose 
less, and presently begin to gain again. The times, then, at 
which our views of the Moon will differ most in consequence 
of its varying speed in its orbit are times when it is in cer- 
tain places in its orbit, one between perigee and apogee, and 
the other between apogee and perigee. These places may of 
course be calculated mathematically, but cannot be readily 
described except in mathematical language. It may here be 
noticed that the Sun, or any celestial object, may be said, like 
the Moon, to be in perigee when it is nearest to the Earth, and 
in apogee when farthest from it. 

The Moon < ront to some extent, with respect 

to the Earth, in other ways besides this. To understand 
them, let us SU] before (176), one of the Moon's 

d diameters in the plane of the ecliptic, and an 
imaginary globe with the Moon's orbit for its equator and 
one of its equatorial diameters also in the plane of the eclip- 
tic. Now it is a singular fact that on this supposition the 



104 Outlines of Astronomy. [Sec. 178. 

two equatorial diameters just mentioned always lie along 
nearly the same straight line, so that if cither the Moon or 
our imaginary globe were to be tilted so as to bring its whole 
equator into the plane of the ecliptic in the manner already 
explained, the line o( the axis round which this movement 
took place would be about the same in both cases. But the 
two movements would be contrary to each other ; thai 
the Moon would have to tilt one way through about 
whole rotation and the globe would have to tilt the other 
way through about fa of a whole rotation in order to bring 
both their equators wholly into the plane of the ecliptic. Both 
these supposed movements are of a kind which cannot be 
called either direct or retrograde ; for the axes upon which 
they are performed lie in the- plane of the ecliptic, and so 
have no northern or southern ends with regard to th.it plane. 
But we have agreed to distinguish between direct and retro- 
grade movements by means of the plane of the ecliptic (1 . 
and therefore cannot conveniently distinguish between them 
by any other plane, even that of the Karth's equator. 

179. We see, then, that if we suppose the Moon to tilt far 
enough to bring its equator into the plane of its orbit instead 
of into the plane of the ecliptic, it would have to move first 
through about -jJ lT and then through about J 2 of a whole 1 
tion round one of its equatorial diameters as an axis. The 
sum of -5^5- and fa is about fa ; but fa would come closer to 
the actual fraction of a rotation needed for the purpose just 
stated. To express the same fact in the usual manner, we 
say that the inclination of the Moon's equator to the plane of 
its orbit is nearly 6j degrees. 

180. Now, since the Moon's poles do not take part in its 
rotation on its axis, and since the effect of that rotation on 
places near either pole is only to make them travel round it 
in a small ring, we sometimes see more and sometimes less 
of the region round either of the Moon's poles ; and this 
would happen even if the movement of the Moon round the 
Earth were uniform and circular. If a man walks round a 
tree with one side always towards the tree, but always lean- 



Sec. iSo.] Planets. 105 

ing a little towards the south, then the top of his head will 
be turned somewhat towards the tree when he is north of 
it. and somewhat away from the tree when he is south of it. 
We have already seen, in considering the Sun (59), that 
sometimes one and sometimes the other of its poles is on 
the disk which it shows us ; and we may here mention that 
the inclination of its equator to the plane of the ecliptic, on 
which this effect depends, is about 7 degrees, or a little more 
than the inclination of the Moon's equator to the plane of its 
orbit round the Earth. The difference between the Moon 
and Sun in regard to the alternate appearance upon their 
disks of the regions close to their northern and southern 
poles is only that the Moon goes round the Earth, while 
it is the Earth which goes round the Sun. 

The Moon's motion in its orbit is only one of the nu- 
merous movements into which its complicated course has been 
lived. Another of these movements, which we are now 
to consider, is represented by a change of the following kind 
in the plane of its orbit. Suppose the imaginary globe, the 
equator of which is the orbit of the Moon, to have a preces- 
sional motion like that of the Earth, but quicker, so that it 
may be completed in the time of the Earth's nutation ; the 
change thus made in the plane of the Moon's orbit is that 
actually assumed to be taking place. The Moon itself has 
a precessional motion, completed in just the same time, so 
that whenever one of its equatorial diameters comes into the 
plane of the ecliptic the line of that diameter nearly agrees 
h the line drawn in the plane of the ecliptic across the 
orbit of the Moon (178). This last line is called the line of 
the nodes of the Moon's orbit ; and the precessional motion 
of that orbit, just mentioned, occasions what is called the 
retro-radation of its nodes. The word precession is usually 
em- l . 1 k i n lt <>( those changes in the view we 

have of cel< 3 which are occasioned by what may 

be called the retrogradation of the nodes of the Earth's equa- 
as Q>S4 I in different terms (107). In like 

manner, the preecs.sional motion of the Moon itself may 



106 Outlines of Astronomy. [Sec. 182 

be called the retrogradation of the nodes of its equato: 
Not only, then, does the Moon rotate once on its axis in 
the same time in which it goes once round its orbit, but the 
nodes of its equator retrograde, generally speaking, with the 
nodes of its orbit. These two remarkable cases of agree- 
ment in period between different motions of the Moon have 
been carefully studied, but have never been fully explained, 
although certain suppositions with regard to the Moon's 
condition in past ages enable astronomers to account for 
the continuance of these agreements, if not for their origin. 

182. The precessional movement of the Moon does not 
alter the inclination of its equator to the plane of the ecliptic, 
and therefore does not increase or diminish the amount by 
which it changes front, so to speak, towards the Earth. It 
merely alters the times at which we have views of the Moon 
differing as much as may be from each other. But any alter- 
ation of the inclination of the Moon's equator to the plane of 
its orbit alters the amount of this change of front. Such 
alterations result from changes cither in the inclination of 
the Moon's orbit, or in the inclination of its equator, to the 
plane of the ecliptic. The effects of these changes may be 
compared to those of the change of obliquity of the ecliptic, 
and of nutation in latitude, in the case of the Earth. Their 
amount is never great. 

183. The Moon is far enough from the Earth to make the 
views of it obtained at the same time in different terrestrial 
stations almost, but not exactly, the same. Moreover, we 
are carried past it every day, by the Earth's rotation ; and 
when it first comes in sight, or, as we say, when it is rising, 
we can see a little more of the region near its preceding 
limb, and less of that near its following limb, than we can 
afterwards. When it sets, the opposite effect takes place. 
The words disk and limb, preceding and following, are used 
of the Moon and of other such objects just as they are of the 
Sun (49). 

184. The Moon's orbit is regarded as in a constant state 
of change in various ways, and in particular as having a 



>r. 



Sec. 1S4.] Planets. 107 

direct revolution of its own, which carries the perigee com- 
pletely round the Earth in about 9 years. This movement, 
like the retrogradation of the nodes of the .Moon's orbit (181), 
s not affect the amount of what we have called the .Moon's 
change of front to the Earth. This change of front, however 
caused., is called libration. The chief causes of the Moon's 
libration are. as we have seen, its varying speed in its orbit, 
and the inclination of its equator to that orbit. By means of 
this Libration considerably more than half the Moon is turned 
towards the Earth at one time or another. 

185. Many comparatively small modifications of the prin- 
cipal movements of the Moon have been noticed and studied 
and still continue to attract much attention ; 
but they nee I not here be described. It is obvious that, in 
addition to its movements with respect to the Earth, the 
Mooo accompanies the Earth in its movement round the 
Sun, and in such movements as may be common to all bodies 
of t em. When we examine the movement of 

the Moon with respect to the Sun, without resolving it into 
a movement of the Moon round the Earth and a movement 
ofl>oth together round the Sun, we find that the Moon's path 
intly concave towards the Sun. That is, if a straight 
line is drawn between any two places in this path very near 
each other, the middle of this line will be between the Sun 
and cordingly, when the Moon is between the 

th and the Sun. its path bends towards the Sun rather 
than towards the Earth. If the Earth were stopped in its 
• the Sun, the Moon would not stav in its neigh- 
» on circulating about the Sun in a less, 
complicated path than that in which it now moves as the 
satellite of the Earth. 

WGi I ' ince from the Earth has been stated 

.bout 30 dian :h. or something 

the Sun. If we draw a circle 

• enough to reach across 

this page, the Sun must be represented by a dot less than 

ifo of the width of ti. ind the Earth and Moon, with 



108 Outlines of Astronomy. [Sec. 186. 

all the space between them, would not fill the width of the 
line drawn to bound the circle, if they were to be represented 
on the same scale ; so that the Moon's orbit would not appear 
distinct from the Earth's, but would be represented by the 
same line. The Moon's diameter is little over a quarter, 
its bulk little over a fiftieth, and its mass little over a hun- 
dredth of the Earth's. It thus appears that the Moon has 
comparatively little density. 

1H 7o The disk of the Moon is circular in shape, according 
to the most accurate measurements which have been made 
of it. So far as can be seen, then, the Moon is spherical, or 
almost spherical, in form. But its precessional movement, 
or the retrogradation of the nodes of its equator (181), could 
not be accounted for by the laws of motion on the SUpp 
tion that its mass is evenly distributed about its centre. We 
must suppose, then, either that the density of its different 
parts varies considerably, or that it is spheroidal in form, 
with its Longest diameter pointing to the Earth. This list 
supposition is generally accepted. Some have supposed the 
sides of the Moon nearest and farthest from the Earth to be 
of slightly different shapes. This theory has been supported 
on purely mathematical reasons, and also on conclusions 
drawn from the examination of photographs taken at such 
times that the effect of libration (1S4) might make the photo- 
graphs differ from each other to some extent. In this man- 
ner, what are called stereoscopic pictures of the Moon, 
showing it as a globe and not merely as a disk, may be pro- 
duced. However, neither the mathematical nor the pli 
graphic grounds for the theory of the unlikeness in shape 
between the two halves of the Moon have proved satisfactory 
to those who are competent to discuss questions of this kind ; 
but all agree that the Moon is not spherical, and that its 
longest diameter points, generally speaking, towards the Earth. 
Attempts have been made to account for this fact, but nothing 
definite is known upon the subject. Whenever the Moon's 
various movements have pointed its longest diameter slightly 
away from the Earth, it must begin to swing back towards 






Sec. 1S7.] Planets. 109 

the Earth ; and the movements thus set up have been called 
real libration of the Moon. But this part oi the Mo. 

libration is known rather by theory than by observation. 

1**. The risible parts of the Moon are undoubtedly solid. 
No distinct signs of any liquid or gas have been discovered 
on the Moon ; and it is probable that no sea and no atmos- 
phere exist there. This is given occasion for many guess 
about the condition of the Moon in past ages, which need not 
here be repeated, since none ot them can as yet be proved to 
be correct. It has been thought that liquids and may 

St upon the Moon in underground cracks and caverns, 
enough, or on the side never seen from the 
Earth, which is less likely. The Moon's mass is perhaps 
too small to keep any noticeable amount of atmosphere 
about it. 

iv>. \V • ,ve see of the Moon is a rugged and mountain- 
ous tract of country, which looks comparatively bright, with 
.rker and smoother districts, which got the name 
of seas and lakes before it was discovered that they were 
only valleys or table-lands. Some of them are farther from 
the Moon's centre, or, as we should say of similar terrestrial 
g er than others are. The Moon's mountains, 
or the lunar mountains, as they are often called, have been 
named ai as men, some of these names being rather 

absurd. Among the lunar mountains are some which are 
Jiest terrestrial mountains. Many 
lunar m have th»» appearance of terrestrial volcan- 

in bet, the volcanic appearance of the Moon is its most strik- 
j peculiarity. But none of the lunar volcanoes appear to 
be active at there are 1 of smoke or fire 

about them. -appose that thev have 

long been extin nera have at times suspected 

that some o* | active, but tl 

iave not l>een confirm* 
!'>'>. rhe most powerful telescopes yet constructed 
us the M t would appear to the naked eye from a 

tance of about forty miles. But in thus ma \ the 



no Outlines of Astronomy. [Sec. 190. 

Moon, we also magnify to the same extent that part of the 
Earth's atmosphere through which we look. Now this 
atmosphere is by no means perfectly transparent or perfectly 
alike in all its parts ; and when we look through it with tele- 
scopes fitted with eye-pieces of great magnifying power, our 
view is apt to be very indistinct and unsatisfactory. Conse- 
quently we never see the Moon nearly as well as we see 
objects forty miles off without the help of any instrument ; 
and with such eye-pieces as are usually applied even to lai 
telescopes, we see the Moon in the proportions of a terres- 
trial object 300 miles or more away, and viewed without a 
telescope. No one, therefore, need expect for the present to 
be able to see animals or buildings upon the Moon, even 
supposing that there are any to be seen there. Considerable 
changes, such as the tailing of great masses of rock, may 
occur in the lunar mountains, without being visible to us. 
There is no certainty that any change of this kind has taken 
place since men began to observe the Moon, although such 
changes have been suspected. 

191, The rock of which the lunar mountains are composed 
does not seem to be very white or polished If it were, the 
Moon would reflect more sunlight, and so appear brighter 
than it actually does. In fact, as any one may see for him- 
self when the Moon is above the horizon by day, it is hardly 
as bright as a cloud lighted up by the Sun, and not much 
brighter than an ordinary terrestrial rock in full sunlight. 
The distance of the Moon, according to the principles of 
optics, does not make any difference in its brilliancy, so that 
we may fairly compare it with clouds and rocks. The lunar 
mountains, probably on account of the manner in which they 
catch the light as well as on account of the material of which 
they are composed, look brighter than the plains beside 
them ; and when the Moon is full, that is, when the Sun 
shines directly on the side of the Moon turned towards the 
Earth, the limb of the Moon looks brighter compared with 
the centre of its disk than it would if it were not for its moun- 
tains. Smaller hills would have the same effect, if they were 






Sec. 191.] Planets. hi 

as steep as these mountains, which are thought to be ordina- 
rily much Steeper than terrestrial mountains. On the whole, 

then, the Moon sends us less light than we are apt to sup- 
pose when we see it by night. But we must remember that 
the western clouds often look very bright just after sunset, 
although there is then too much light in the sky to let us see 
the stars ; so that it is not surprising that the Moon looks 
bright when the night has fairly begun. According to such 
comparisons as have been made, half a million full moons 
would not send us as much light as the Sun does. But par- 
ticular parts of the Moon shine so brightly that we may pre- 
sume that they consist of white or of polished rock. 

192. We get some heat from the Moon, but very little. 
This heat, SO far as it makes its way through our atmos- 
phere, which stops most of it, may be measured by the ther- 
mopile (97) ; and careful measurements of this kind have 
la; civ been made. They show that the Moon probably gives 
out no heat of its own. The rocks upon it reflect some of 
the Sun's heat to us. and besides this, they become very hot 

le the Sun shines upon them, as it does for a fortnight at 
a time, owing to the slowness of the Moon's rotation on its 

i. They have little or no atmosphere in their neighbor- 

1 to stop part of the heat of the Sun on its way to them, 
and probably become much hotter than boiling water before 
the Moon's rotation begins to turn them away from the Sun. 
These hot rocks send out heat while they are cooling off as 
well as while they are exposed to the Sun. But the chief 

:t of the heat sent out by the Moon towards the Earth is 

off clouds in the Earth's atmosphere, and even this 

effect is not very noticeable, although it can be perceived. 

en it takes place, the rocks and soil of the Enrth can 
send out th< irithout having it reflected back to them 

the clouds, and so irrow cooler rather more quickly than 

they do on clou Hence the heat sent us by the 

re apt to make us cool than to warm us. The 

hi from a bright star is more easily perceived 

anci measured than the very small amount which we receive 



ii2 Outlines of Astronomy. [Sec. 192. 

from the Moon ; but our knowledge of these minute quanti- 
ties of heat is still very imperfect 

193. The Earth, since it is larger than the Moon, sends 
more light and heat to it than comes from the Moon to the 
Earth. In fact, the light by which, at the time of new moon, 
we see that part of the Moon's disk on which the Sun is not 
shining, is sunlight reflected from the Earth to the Moon, 
and then back from the Moon to the Earth. At such ti: 
we may notice that the bright part of the disk seems to be 
part of a larger disk than that to which the faintly lighted 
part belongs. This is due to the blurring or spreading out 
of any bright object as it appears to our eyes. An effect of 
the same kind h above (80). Blurring of 

this kind is called irradiation ; there are other sorts <A blur- 
ring, which are mostly due to the air through which we look. 

194 Even the smallest teleso fh of the 

Moon's mountains and plains to make it an interesting 
object to examine. But little interest will be found in 
merely looking over the Moon even with the best tel< 
If our object is only to amuse ourselves, we must still com- 
pare the objects we see with their forms shown on 
map of the Moon, and learn to recognize them under the 
various appearances which they put on according to the 
different ways in which the sunlight falls upon them at one 
time or another. At times when the Moon is visible, but 
not full, we see with any telescope, and occasionally without 
one, that the boundary between that part of it on which the 
Sun shines and the remainder is uneven. The line of this 
boundary on the Moon's disk is called the terminator, and is 
uneven because the region it crosses is rugged, so that the 
sunlight is cut off from the low ground by the hills. In 
those places where the terminator crosses one of the plains, 
called seas, it looks more even than elsewhere. Beyond the 
terminator we usually see a number of bright specks, which 
are mountain-tops lighted up by the Sun, while the valb 
lying between them and the terminator are in the shade. 
The bright regions near the terminator are marked with dark 



THE MOON. 



Plate IV. 



£AST r >H 




^-- 







» I.11I1 II? \. 



The principal features of the Moon, many of which may be recog- 
nizee! by the naked eye, are shown in this figure. When the Moon is 
about three-quarters full, the range of mountains bounding the Sinus 
Iridum may be seen, without a telescope, to project beyond the ncigh- 
che terminator. Bright streaks are shown about the 
mour. nicus, but not about Tycho, where they could not 

easily be drawn. The places of the range called the Apennines, and 
of the mountain Plato (see Plate V.), are also shown in this figure. 






Plate V. 




>hown inverted, as it appears in a telescope 

Of the terminator appears ill the lower right-hand corner. On the plain 
within Plato appear the shadows of the peaks along its left-hand border 



Sec. 194.] Planets. 113 

shadows cast by mountains, the height of which is shown by 
the length of these shadows. In fact, our knowledge of the 

f lunar mountains depends on the accurate measures 
which have been made of their shadows. Farther from the 
terminator the shadows are shorter, because the mountains 
which cast them are turned more directly towards the Sun ; 
so that many lunar mountains cannot well be distinguished 
except when they are near the terminator. But certain bright 
streaks on the Moon can be seen best under full sunlight, and 
are consequently plainest at the time of full moon. These 
streaks extend every way from some particular mountains, 
cially from one named Tycho. 
195. The planet Mercury, which we are next to consider, 
is about fa as far from the Sun as the Earth is; and conse- 
quently, by Kepler's third law, it must go round the Sun 
about four times in one of our years. It is rather larger and 
much denser than the Moon, its diameter being about f as 
long and its mass about ^ as great as the Earth's. The 
eccentricity of its orbit is about \, so that at perihelion it 
is about I as far from the Sun as at aphelion. The inclination 
of its orbit to the plane of the ecliptic is about 7 degrees ; in 
other words, if there were a great globe enclosing the Sun, 
With the orbit of Mercury for its equator, that globe would 
have to make about ^ f of a rotation, round that one of its 
equatorial diameters which would lie in the plane of the 
ecliptic, in order to brin^ its whole equator into that plane. 
The line of the equatorial diameter used as the axis of this 
rotation is called the line of the nodes of Mercury's orbit. 
My spheroidal in shape ; however, it is diffi- 
cult to measure accurately the small disk which it shows us. 
thought they could see indications of its 
>es rotate, but we do 

not ' ed rotation occupies, or. indeed, 

moot say positively, therefore, 

r or poles. It is not known to have an 
atmosphere. :' mountains have been perceived upon 

1 ; but recent observations show only 
8 



ii4 Outlines of Astronomy. [Sec. 195. 

that we know nothing about these mountains, and cannot 
even tell, when we examine Mercury with our telescopes, 
whether we are looking at land or clouds. 

196. Venus is about ^ as far from the Sun as the Earth 
is ; it goes round the Sun, in a nearly circular orbit, in about 
^0 of a year. The inclination of its orbit to the plane of the 
ecliptic is about 3} degrees ; that is, the orbit would be 
brought wholly to the plane of the ecliptic by about T ^ of 
a rotation round the line of its nodes as an axis. The shape 
of Venus is spherical, so far as can be seen ; its bulk is about 
jfa but its mass only about * 6% of the Earth's, so that the 
Earth is a somewhat denser object than Venus. However, 
it is not known that the measurements yet made of the disk 
of Venus are any thing more than measurements of the dis- 
tance between clouds on opposite sides of the planet If this 
is the fact, Venus may not be quite so large a body as is sup- 
posed at present, and it may therefore be denser than we now 
take it to be. Venus is tolerably well known to have an 
atmosphere, and perhaps there are clouds in this atmosphere ; 
but whether these clouds are numerous enough to shut out 
our view of the planet which they surround has never been 
discovered. Several observers have thought they saw si| 
upon Venus of mountains, and of a movement of rotation ; 
but later observations show that these signs cannot usually be 
seen, and we must conclude that although Venus sometimes 
comes nearer to the Earth than any other of the principal 
planets ever does, we cannot find out much about it. 

197. The reason why we know little of Venus and Mercury 
is that they are nearer to the Sun than the Earth is. When 
Venus or Mercury is on one side of the Sun. as seen from the 
Earth, it looks in a telescope like a half-moon, because the 
Sun lights up only half of that side of the planet which is 
turned towards the Earth ; and when either of these planets 
is nearly between the Sun and the Earth, the Sun hardly 
lights up any part of it of which we are in sight. These 
changes, however, may sometimes help as well as hinder our 
observations ; for many parts of the Moon are best seen at 



Sec. 197.] Planets. 115 

other times than when it is full : the great difficulty in observ- 
ing Mercury and Venus is that we never see them far on 
eith f the Sun. If we stand outside of a field in which 

there is a tree, we cannot usually see any thing in the held if 
we look far away from the tree. Suppose we are north of the 
field, and far away from it ; then if we look east or west, we 
entirely lose sight of it. But if we go into the field; we can 
have the tree behind us and part of the field in front of us at 
the same time. Now, as we are always outside the orbits of 
Venus and Mercury, we can never see those planets unless 
we look pretty nearly towards the Sun at the same time. We 
must therefore observe them by day, or else at times when 
they have just risen or are near setting ; and then we have to 
look through so much of the Earth's atmosphere that it is 
difficult to see any thing distinctly. 

19S. Planets nearer the Sun than the Earth is are called 
inferior planets. Venus and Mercury are the only inferior 
planets which are known : but black spots have sometimes 
been seen crossing the Sun's disk, which have been sus- 
pected to be small planets near the Sun. However, astrono- 
mers have looked carefully for such planets during total 
eclipses of the Sun, when they would be most likely to be 
in the Sun's neighborhood, without discovering any. 
199. Planets farther from the Sun than the Earth is are 
called superior planets. Mars is the nearest of these to the 
th ; it is about half as far again from the Sun as the 
th is. and occupies nearly two years in going once round 
the Sun. The eccentricity of its orbit is nearly ^ ; that is, 
hi from the Sun at its perihelion as at its 
linn. The length of a diameter of Mars is rather moie 
than half as j the length of one of the Earth's diam- 

:nc^ its bulk is over J, while its mass is less than j, 
• trth's. [t9 density, therefore, is less than that of the 
tly spherical ; but how far its 

1 that of a sphere has not yet been deter- 
mined, as the measurements of different observers do not 

th each other. The orbit of Mars is little inclined to 
the j the ecliptic. 



n6 Outlines of Astronomy. [Sec. 200. 

200. The Earth is evidently nearer to Mars when it is 
nearly between Mars and the Sun than it is at other times. 
But our distance from Mars, when the Earth comes nearly 
between it and the Sun, greatly depends on the place of 
Mars at that time in its somewhat eccentric orbit. If it is 
then near its perihelion, it will be nearer to the Sun, and 
therefore nearer to the Earth, by \ of its mean distance from 
the Sun, than it would be if it were then in aphelion. If the 
Earth is at its aphelion when it comes nearly between the 
Sun and Mars, it will pass somewhat nearer Mars than if it 
is at its perihelion ; but the eccentricity of the Earth's orbit 
is small compared with that of the orbit of Mars. When 
Mars is nearest to the Earth, it is to be seen from that side 
of the Earth which is turned away from the Sun, as has just 
been shown ; so that it rises about sunset and can be ob- 
served in the night. Besides this, the Sun then lights up 
that side of Mars which faces towards the Earth. Accord- 
ingly, much more has been learned about Mars than about 
Venus, although when Venus is between us and the Sun it 
comes nearer to us than we ever do to Mars. There are 
several dark spots on Mars, which have often been seen in 
the course of the last two centuries. These spots appear 
now to be of about the same shape which former observers 
give them in their drawings of Mars, made long ago ; so that 
it is reasonable to conclude that we see something like firm 
land on Mars, and not merely clouds in its atmosphere. But 
Mars has an atmosphere, probably containing watery vapor, 
as is shown by observations with the spectroscope ; and 
most likely there are times when the clouds in this atmos- 
phere cut off our view of the land which it surrounds. This 
will explain why the spots on Mars seem sometimes to have 
various and changeable shapes, unlike those which are seen 
at other times. Those spots which have been often seen in 
about the same shapes, and which are therefore not likely to 
be the effect of clouds, are supposed by some observers to be 
oceans and seas. Most of the remainder of the disk^has a 
reddish tint, so that Mars looks like a red star when viewed 



Sec. 200.] Planets. 117 

without a telescope ; this may perhaps be due to the color of 
its soil and rocks. By watching the spots of Mars we learn 
that it has a direct movement of rotation upon an axis. This 
makes the spots seem to cross the disk of the planet. The 
time in which Mars completes one rotation is little more than 
one of our days, and the statements of its amount made in 
recent times by different astronomers differ only a small frac- 
tion of a second from each other. From observations of 
this kind the places of the axis and equator of Mars have 
been pretty nearly made out, and it appears that the equator 
of Mars is inclined to the plane of its orbit about as much as 
the Earth's equator is inclined to the plane of the ecliptic. 
But it is more difficult to determine this accurately than to 
find the time required for one of the rotations of Mars. 

201. Sometimes the region near the north pole of Mars 
appears upon the disk of the planet (59, 180), and sometimes 
the region near its south pole is the nearer of the two to the 
Earth. These polar regions, whenever seen, are observed to 
be white ; and when either of them has been turned away 
from the Sun for several months by the planet's change of 
place in its orbit, the white spot on that part of Mars is 
larger than it is when the same region has been turned 
towards the Sun. This makes it probable that there is some- 
thing on Mars like what we call snow and ice, and that the 
climate of Mars is warm enough to let this snow melt in 
the sunshine. However, the white substance seen about the 
poles of Mars cannot be proved at present to be exactly like 
terrestrial snow. The disk of Mars is comparatively bright 
all round the limb ; this may be due to the effects produced 
by clouds. 

202. Hardly any thing is known of the small planets be- 
tween the orbits of Mars and Jupiter (108) except the form 
of the orbit of each of them and the position of its plane with 

lect to that of the ecliptic. The most eccentric of these 
orbits 1. istauce between its foci equal to about £ of 

the major axis ; that which is most inclined to the plane of 
the ecliptic would be brought into that plane by about A \ of a 



n8 Outlines of Astronomy. [Sec. 202. 

rotation round the line of its nodes as an axis. However 
many asteroids there may be, the mass of all of them taken 
together must be small, as has been shown by the study of 
the movements of the other planets. The asteroids nearest 
the Sun are not much over twice as far from it as the Earth 
is ; the mean distance of those which arc most remote is about 
3J times that of the Earth. A few asteroids look a little hazy 
or blurred, and have been thought on this account to have 
atmospheres ; but most of them show no disks at all, and 
look just like faint stars, invisible except in good lelesco 

203o The four great planets, Jupiter, Saturn, Uranus, and 
Neptune, go round the Sun in orbits of little eccentricity, the 
planes of which differ little in position from the plane of the 
ecliptic. The mean distance of Jupiter is about 5 times that 
of the Earth ; that of Saturn about 9A, of Uranus about 
of Neptune about 30, times that of the Earth. Saturn is 
therefore nearly twice as far as Jupiter from the Sun. and 
Uranus twice as far as Saturn ; but Neptune is not much 
more than once and a half as far as Uranus. The comj 
tive mean distances of all the principal planets as far as 
Uranus can be expressed pretty well by a rule commonly 
called Bode's law. According to this law, we count the 
distances of the planets in tenths of the Earth's mean dis- 
tance. If we take 4 from the number of these tenths which 
denotes the mean distance of any planet beyond Mercury, 
double the remainder, and add 4 to the product, we shall 
have the mean distance, according to Bode's law, of the next 
planet beyond that which we begin with. Mercury is about 
4 tenths and Venus about 7 tenths as far as the Earth from 
the Sun. Taking 4 from 7, we have 3 : twice 3 is 6 ; 6 and 
4 make 10, which is of course the Earth's mean distance 
counted in tenths of itself. Adding 4 and 12, we have 16 for 
the distance of Mars ; 4 and 24 make 28 ; and the sum of 
4 and 48 is 52, which represents Jupiter's distance very well. 
Saturn's distance does not fall far short of that denoted by the 
sum of 4 and 96, or 100 ; while 4 and 192 make 196, which 
answers well to the distance of Uranus. But 4 and 384 make 






Sec. 203.] Planets. 119 

3SS, and the mean distance of Neptune is only 300 tenths of 
the Earth's mean distance. The want of a planet between 
Mars and Jupiter, to satisfy the rule just stated, was noticed 
re any asteroids were discovered ; the mean distances of 
the first asteroids which were found are about 27 tenths of the 
Earth's mean distance, so that the discovery made it likely 
that the distances of any planets there might be beyond 
Uranus would conform to Bode's law ; but when Neptune 
was discovered, its distance was found to be much less than 
would have been expected. We should have to add to Nep- 
tune's mean distance more than a quarter of its actual amount 
to make it as great as it would be according to Bode's law ; 
the law, however, may be hereafter explained by more gen- 
eral laws, so as to show why it does not hold good in the 
of Neptune. 
204. Jupiter is the largest of the known planets, its diam- 
eter being over ten times as great as the Earth's. If its 
density were as great as the Earth's, its mass would be much 
over a thousand times that of the Earth. In fact, however, 
Jupiter weighs not much over three hundred times as much as 
the Earth, so that its density is small. But it is most likely 
that we see little of Jupiter except clouds in its atmosphere ; 
and these clouds may extend so far as to make the planet 
than it would appear without them. 
!iin the clouds, therefore, there may be matter of con- 
siderable density. Jupiter occupies nearly twelve years in 
goinij once around the Sun. 

Ic of Jupiter is crossed by dark streaks, called 

belts, which fade urds the limb, and frequently change 

their form and 1 it some of the spots and markings 

long enough to show very plainly that 

tea on an axis. Its movement of rotation is 

din- that a whole rotation is completed in a 

in ten hours. Each belt, speaking generally, is 

' ir in one ?- from either of Jupiter's poles ; 

the belts are arranged like what art- called /ones in 

geo_ The quick rotation of Jupiter probably has 



120 Outlines of Astronomy. [Sec. 205. 

something to do with this arrangement of its belts, and also 
with its general shape, which is so far from being exactly 
spherical that an equatorial diameter of the planet is greater 
than the polar diameter by about ^y of its own amount. The 
spots of Jupiter from which its rotation is determined shift 
their places to some extent with respect to each other, so 
that the exact time of rotation is difficult to make out, as 
happens for a like reason in the case of the Sun (60). If 
the spots of Jupiter are caused by the difference of darkness 
between different clouds, or between clouds and the solid 
part of the planet, it is natural that they should shift their 
places considerably. However, different estimates of the 
time in which Jupiter makes one rotation agree together 
within a few minutes. Jupiter's equator lies nearly in the 
plane of its orbit. 

206. Like Mars, and the other superior planets, Jupiter is 
nearest to us when the Earth comes nearly between it and 
the Sun. But even then, since it is over live times as far from 
the Sun as the Earth is, it is over four times as far as the 
Sun from the Earth ; so that its diameter does not seem 
but less than fa of the Sun's. Without a telescope, then, we 
cannot see that it shows any disk at all ; it only appear 
be a star brighter than any other except Venus. If we sup- 
pose it to be surrounded by clouds, we can see why it should 
look bright compared with Mars ; for most of the suni 
by which we see Mars has been twice through that planet's 
atmosphere, once on its way from the Sun to Mars, and again 
in coming from Mars to the Earth ; while the clouds around 
Jupiter- probably reflect much sunlight to us before it has 
entered the denser parts of Jupiter's atmosphere. We have 
seen that an atmosphere is apt to absorb (51) part of the 
light which passes through it ; hence, although Mars is 
nearer the Sun than Jupiter, so that it must receive more 
sunlight in proportion to its bulk, and in fact does look like 
a bright star when it is nearest to the Earth, Jupiter looks 
still brighter even when the Earth is not nearly between it 
and the Sun. But if Jupiter were not far larger than Mars, 



Sec. 206.] Planets. 121 

its brightness would not be enough to make up for its dis- 
tance, and it would seem like a small star ; not that it would 
then be dimmer than it now is, but because we judge of the 
brightness of seemingly small objects by the whole amount 
of light they send us as much as by the brightness of their 
separate parts. Jupiter is usually yellowish white, but some- 
times reddish. In 1S70, for instance, it was decidedly reddish 
for a time. 

207. Jupiter has four satellites, which revolve about it as the 
n does about the Earth. These satellites are bodies of 
about the bulk of the Moon and Mercury, which are not very 
different in size, as we have seen (186, 195). Their orbits 
round Jupiter are almost in the same plane with Jupiter's 
equator, and as this equator is nearly in the plane of Jupiter's 
orbit, which does not differ greatly from the plane of the 
ecliptic (203), it follows that the orbits of Jupiter's satellites 
are pretty nearly in the plane of the ecliptic. Accordingly, 
these satellites are always near that plane ; and as we also 
are always near it, we look at their orbits edgewise. For this 
reason Jupiter's satellites seem to us to move straight across 
the disk of Jupiter or behind it, always coming back to the 
disk after going a certain distance one way from it or the 
other. Consequently, they are often hidden from us in 
Jupiter's shadow or behind its disk, and we often see them 
or their shadows upon that disk. Their orbits, when made 
out by calculation from their observed movements, are found 
to be nearly circular, and their motion in these orbits is direct. 
There are certain fixed relations between their places and 
also between their movements, partly accounted for by known 
laws of motion. Their brightness changes considerably from 
time to time. Someti- tellite of Jupiter, when it passes 

between us and the planet, looks like a dark spot on Jupiter's 
disk ; sometimes like a bright spot ; and sometimes is too 
nearly of the same brightness with the disk to be seen at all. 
Some observers have thought that each satellite is always 
brightest at some particular part of its orbit, and from this it 
3 been concluded that Jupiter's satellites rotate on their 



122 Outlines of Astronomy. . 207. 

axes, each making one rotation in the time it requires to go 
once round Jupiter, just as the Moon makes one rotation 
while it goes once round the Earth ; other observer*, how- 
ever, think differently. But nothing is positively known of 
the rotation of any satellite except that which accompanies 
the Earth. 

208. That satellite of Jupiter called the first is the nearest 
to the planet ; the others are called second, third, and fourth, 
in the order of their distance from Jupiter. The second is 
the smallest, its diameter being rather less than our Moon's ; 
and the third is the largest, considerably exceeding Mercury 
in hulk. The first is somewhat farther from Jupiter's centre 
than the Moon is from the Earths centre, and goes round 
Jupiter once in less than two days : the fourth is nearly lour 
times as far from Jupiter, and completes its revolution in I 
than seventeen days. 

209. Saturn's diameter is about nine times . is the 
Earth's ; so that Saturn resembles Jupiter in size, as it (' 
also in many other ways. It has belts less distinct than 
those of Jupiter, but like them ; each of its rotations, which 
are direct, occupies little more than ten hours ; its shap 
like that of Jupiter, and its density is small ; for its m.h 
less than 100 times the Earth's : hut we must remember that 
in measuring the disk of Saturn, we may be measuring only 
the distance between clouds, and in this way may 1 

mate the bulk and underestimate the density of the planet. 
Saturn's equator is not so nearly in the plane of its orbit and 
in that of the ecliptic as is Jupiter's ; it is about as much 
inclined to these planes as the Earth's equator is. Hence 
sometimes one and sometimes the other of its poles is turned 
considerably more than the opposite one towards the Sun ; 
and its polar regions have been thought to change color to 
some extent, like those of Mars ; but it seems unlikely that 
this is. due to snow. Saturn goes round the Sun once in 
somewhat less than thirty years. 

210. Saturn has eight satellites ; they have been named 
instead of merely being numbered ; but we know little about 



JUPITER. 



Plate VI. 




.nv Lull I If 



This figure represents Jupiter ai it appeared m the telescof* (and 
therefore inverted) at Harvard College Observatory on the evening of 
February 2, 1872. The second satellite has just passed off the disk. 
on which its shadow is still visible. The equatorial region of U* 
planet had a reddish tint, not represented here. 



Sec. 210.] Planets. 123 

them except these names. Their motion is direct, and some 
of them have been thought to rotate once during one revolu- 
tion about Saturn, tor reasons like those which gave rise to 
the same opinion about Jupiter's satellites. The nearest to 
s satellites goes round the planet in less than a 

. and is only about half as tar from Saturn's centre as the 
Moon is from the centre of the Earth ; its name is Mimas : the 
farthest called Iapetus, is nearly twenty times as far as Mimas 
from the centre o\ Saturn, around which it makes little more 
than one revolution in eighty days. Titan, the largest of 
Saturn's satellites, is nearly of the same size with the largest 
satellite of Jupiter ; the others seem to be bodies smaller than 
the Moon, ami some of them can scarcely be seen even with 
large telescopes. Their orbits seem to be nearly in the same 
plane with the equator of Saturn ; but the plane of the orbit 
of Iapetus di tiers less from the plane of the ecliptic than do 
the planes of the orbits of the remainder. 

211. Within the orbit of Mimas is a large flat ring, with its 
inner edge towards the equator of Saturn, which it completely 
surrounds. The part of this ring nearest Saturn reflects 
little sunlight to us. so that it has a dusky appearance, and is 
not easily seen, although it is not quite so dark as the sky 
seen between it and the planet. The outer edge of this 
dusky portion of the ring is at a distance from Saturn of 
between two and three times the Earth's diameter. Outside 
of this dusky part of the ring is a much brighter portion, and 
outside of this another, which is somewhat fainter, but still 
so much brighter than the dusky part as to be easily seen. 
The width of the brighter parts of the ring is over three 
times the Earth' ter. To distinguish between the 

different par* ~ rn's ring the outer part is called ring 

•he middle part ring B, and the dusky part ring C. 
D apparently open space, near 2000 miles 

•. which looks like a black line on the ring. Other divi- 

1 in the ring have been noticed at times, but this is the 
only on' 1 with good tele- I times when 

either side of the ring is in view from the Earth. 



124 Outlines of Astronomy. [Sec. 212. 

212. If Saturn's ring were in the plane of the ecliptic, it 
would always have its edge to us, and then we could scarcely 
see it at all ; for it is perhaps less than 100 miles thick, and 
when its edge happens to be turned towards us. nothing can 
be seen of it except with the best telescopes ; and even these 
show slight signs of it, if any. We could scarcely learn any 
thing about the ring from this view of it alone ; but as the 
planes which bound it are about as much inclined to the 
plane of the ecliptic as is the plane of Saturn's equator, we 
get different views of it at different times. We can easily 
understand the sort of difference which there is between the 
appearances of Saturn's ring at one time and another, if we 
try some such experiment as the following. 

213. Let some one hold a book with one side upwards and 
the other downwards at about the height of his head ; that is, 
the book is to be placed as it would be if it were lying on the 
table, except that it is to be higher from the floor, so as to be 
nearly on a level with the eyes of any one standing in the mid- 
dle of the room. Let the upper cover of the book be lifted about 
one-third as far as would be necessary to make it stand upright ; 
in other words, let this cover be carried through about one- 
twelfth of a whole rotation about the axis on which it turns 
when the book is opened. Then, if we take the upper leaf of 
the book to represent the position of the plane of Saturn's 
orbit, the position of the cover will represent that of the plane 
of Saturn's ring. Now let the book be carried round the room 
so as always to keep its place with regard to the points of 
the compass ; that is, if the upper edge of the cover was at 
first pointing north and south, let it be kept pointing north 
and south while the book is carried round the room. Any 
one who watches this movement from the centre of the room 
will always have the edge of the upper leaf of the book turned 
towards him ; and the edge of the cover will also be turned 
towards him twice before the book has been brought back to 
its first place. But at all other times either the outside or 
the inside of the cover will be turned towards him. In the 
same way, if Saturn's ring nad no inclination to the plane of 



Sec. 213.] Planets. 125 

its orbit, its edge would always be turned towards the Sun ; 
while, on account ot its actual position, its edge can be 
turned to the Sun only twice during the time which Saturn 
occupies in going once round the Sun. Hence one side of 
urn's ring is continually lighted up by the Sun for nearly 
en years, while the other side remains in the shade. At 
the end of this time the edge of the ring has again been brought 
the Sun ; and afterwards, for another period of nearly 
fifteen years, the Sun shines upon that side of the ring pre- 
viously in the shade, while the side formerly lighted up is now 
dark. 

214. Accordingly, by an observer in the Sun, one side or 
the other of Saturn's ring would always be seen, except when 
Saturn was at one or the other of two opposite places in its 
orbit. But the edge of the ring may be turned towards the 
Earth more frequently than towards the Sun. To show this, 
let a book be carried very slowly round the room in the man- 
ner already described, while one observer watches it without 
leaving his place in the middle of the room, and a second 
observer walks round him at a short distance, moving the 
same way as the person who carries the book, and more 
quickly than that person. When the book has been brought 
nearly, but not quite, to one of those places in which the edge 
of it is turned towards the stationary observer, it will 

often happen that the second observer comes to a place from 
which he sees the cover e while one of its sides, the 

outside for example, is still in view from the middle of the 
room. As he continues his course, he will be for a short 
time in sight of the inside of the but may perhaps 

:n get a •. le of it before its edge lias been 

tur rver. He may afterwards 

continu bt of the outside of the cover a 

the m the middle of the room ; 1 ut 

ill soon bring him to a part of his 
ich he will again see the inside of the cover. 1 

'1 under any Circumstances be turned 
him more frequently than towards the stationary 



126 Outlines of Astronomy. [Sec. 214* 

observer, although this may not happen exactly in the way 
just described ; and the two observers will sometimes see 
different sides of the cover. But unless the observer who 
shifts his place goes far from the middle of the room, both 
observers will always see the same side of the cover except 
about those times when its edge is turned towards the 
stationary observer. 

215. Accordingly, a terrestrial observer has the edge of 
Saturn's ring turned towards him more frequently than it is 
turned towards the centre of the Sun. He is sometimes car- 
ried by the Earth's motion from a place in view of that side 
of the ring on which the Sun is shining at the time to a place 
in view of its dark side ; and the Earth's motion may bring 
him back again to some place in view of the bright side of 
the ring before the Sun has ceased to shine on it. Some- 
times, too, the Earth may come opposite to the ec\<^ of the 
ring, and at once be carried back, by its movement in its 
orbit, to the side of the ring on which the Sun is shining ; 
but when the dark side of the ring is in view from the Earth, 
the Earth will soon come up to the plane of the ring and | 
through it, so as to have the bright side in view ; it cannot 
in this case just come opposite to the edge of the ring and 
fall back again, as it can when it is on the same side of the 
ring with the Sun. All these facts may be readily shown 
by the experiment described above. About the time when 
the edge of Saturn's ring is turned towards the Sun, it may 
be turned in the course of a year once only, twice, or three 
times, towards the Earth. 

216. When the dark side of the ring is in view, it appears 
as a black line crossing the planet ; and on such occasions 
the sunlight reflected from the outer and inner edges of the 
rings A and B enables us to see traces of the ring on each 
side of Saturn, at least in places where two such reflections 
come nearly together. The seven inner satellites of Saturn, 
when the ring has its edge turned nearly towards us, may 
sometimes be seen between us and the ring or beyond it, 
looking like beads on or close beside the fine thread of light 



Sec. 216.] Planets. 127 

to which the ring is then reduced. But at other times, since 
we look at the planes of their orbits, as well as at the 
m one side or the other, and not edgewise, we see 
S itellites in various places around the planet ; and 
their paths, as well as that of the outer satellite, do not 
appear straight like those of the satellites of Jupiter, and sel- 
dom carry them between Saturn and the Sun or Earth. The 
I is of course most conspicuous at a time about half-way 
between the times when its edge is turned towards the Sun. 
Whenever its bright side is in view, its shape appears to us 
elliptical, owing to the effects of perspective, as we should 
call it in a picture. The parts of the ring called its ansa? are 
those about the ends of this seeming ellipse, one of them 
being on each side of Saturn. Ring C, which is somewhat 
transparent, is most easily seen at each ansa ; but it appears 
as a dusky line where the inner edge of ring B comes 
between us and the main body of Saturn, or the ball, as it is 
often called. When the edge of the ring is turned awav from 
us as much as it ever can be, ring A appears all round the 
ball ; but the rings B and C always come between us and 
part of the ball, and are themselves partly hidden behind it. 

How the ring of Saturn can keep its place about the 
planet is a question which it has always puzzled mathemati- 
cians to answer in conformity to the ordinary laws of motion. 
First it appeared that the ring could not be supposed to be 
made of solid matter all in one piece unless the masses of 
different parts of it were different, and unless at the same 
time the whole ring revolved rapidly round the ball ; and this 
revolution of the ring was thought to be shown by observa- 
tion as well as by calculation. But later inquirers satisfied 
themselves that even this explanation was not enough to 
.y the ring did not break to pieces, or fall down in 
some way upon the ball. T jested, then, that the 

-e liquid. Still later, other mathematicians have 
themselves that the ring can neither be solid and in 
one piece, nor yet liquid, if it is to keep its place : and they 
conclude that it must be made up of a great number of small 



128 Outlines of Astronomy. [Sec. 217. 

satellites, each of which revolves around Saturn in an orbit 
of its own, but is always so near other little bodies like 
itself that it does not appear separate from them to ob- 
servers at a distance. This theory is said to account for the 
division between rings A and 13 by considerations founded 
on the laws of motion and the observed place of one of 
the eight distinct satellites of Saturn. It will also explain 
the dusky appearance of ring C by the supposition that the 
small satellites nearest Saturn are not so closely crowded 
together as those beyond them ; and the fact that ring I 
brighter than ring A may probably be due to the great num- 
ber of satellites which we should expect to find in the middle 

part of the ring. Recent spectroscopic observations show 
that the ball of Saturn has an atmosphere, but leave it doubt- 
ful whether the ring has one. Without the aid of any instru- 
ment, Saturn may be seen as a bright star. 

218. Uranus is much smaller than Jupiter or Saturn ; its 
diameter, however, is about lour times that of the Earth. Its 
mass is only fifteen times as great as the Earth's, so that its 
density is about the same as that of Jupiter. NeptUM 
somewhat larger and heavier than Uranus, but not so del 
The time in which Uranus goes once round the Sun is over 
eighty years ; Neptune occupies over one hundred and si 
years in one revolution. Nothing is known of the rotations 
of Uranus and Neptune, or of any difference in length be- 
tween different diameters of either. Some observers have 
thought that they perceived spots on Uranus, but their con- 
clusions with respect to its rotation do not ith each 
other. 

219. Uranus is known to have four satellites, and Neptune 
one. Other satellites have been suspected to accompany 
these planets, which have also been thought to have rings 
like the ring of Saturn. 

220. The known satellite of Neptune is somewhat nearer 
Neptune than the Moon is to the Earth, and goes round 
Neptune once in about six days. Of the -known satellites ot 
Uranus, that which is farthest from the planet is about half 



Sec. 220.] Planets. 129 

jrain from it as the Moon is from the Earth, and goes 

ICC in less than a fortnight The planes of 

the orbits of all I tellites differ considerably from the 

plane of the ecliptic ; the orbit oi Neptune's satellite would 

e to mak. tenth of a rotation round the line 

to be brought into the plane of 
the ecliptic, and more than twice as much rotation would be 
for that purpose by ths orbits ot" the satellites of I'ra- 
An observer near Uranus, then, placed with his feet 
.rds the plane of the ecliptic, would see the planet's satel- 
g nearly over his head (140); so that the words 
do not apply very well to their move- 
ment. But they would not pass exactly over the head of our 
supposed observer ; and if he was on the northern side of the 
: the ecliptic, he could perceive their movement to be 
vhen they passed in front of him ; 
. d to hive a retrograde movement in 
r orbits. Th dent of Neptune's satellite can be 

observed only with much difficulty ; but it seems to be retro- 
j, like the movement of the satellites of Uranus. 
221, Uranus can barely be seen, and Neptune not at all, 
without a telescO] tfe these planets seem to have at- 

and it has been thought that some of the light we 
1 them may proceed from incandescent matter 
belonging to them, and may not be merely sunlight reflected 
to 

Jupiter and Siturn, also, are considered by some 

>ly hot txxlies : but the light they send 

with the spectro- 

.in sunlight. But, as we have seen, 

ly that this light comes from clouds brightly lighted 

up in. 



130 Outlines of Astronomy. [Sec. 223. 



CHAPTER VI. 

NEBULA, COMETS, AND METEORS. 

223. Any cluster of stars too faint to be distinguished 
separately will appear to us, if it can be seen at all, as a 
whitish speck in the sky, which looks like one of the objects 
called nebulae ; and clusters of faint stars are actually called 
nebulae until we are able to make them out to be clusters. 
But it is now generally believed that many of the cloud-like 
objects seen with the help of telescopes are not clusters of 
stars, but collections of luminous gases or clouds of fine par- 
ticles of solid or liquid matter. When an object of this kind 
shines by light of its own, and is so far from us that it seems 
to move very slowly, if at all, it is always called a nebula. 
To be visible at all, it must be larger than a star, since its 
light is not brilliant; and some nebulae certainly stretch over 
vast spaces in the universe ; but no one can tell how large 
these spaces are until we have learned the distance from the 
Earth of the nebulae wliich fill them. It is more difficult to 
determine the distance of a nebula than that of a star, 
because a nebula is an indistinct object, so that its place 
among the stars, as seen from the Earth, cannot be exactly 
made out ; and the distances even of the stars are yet almost 
wholly unknown. But if some of the nebulae are no farther 
from the Earth than the nearest of the stars whose distances 
are known, even then each of them must be large enough to 
reach over spaces much greater than that between the Sun 
and the Earth. 

224. The spectroscope shows us that some nebulae are 
composed of gases, perhaps unlike any which are known to 
chemists ; other nebulae seem to be partly solid or liquid ; 
but perhaps they are wholly gaseous, their gases being for 
some reason so dense in places as to give out light like that 



Sec 224.] Nebula, Comets, and Meteors. 131 

Qt liquid. The forms of nebula? are various ; 

round disks, and may be spherical or nearly 

J in form. These are called planetary nebulae. 

. the shape oi rings, and still others have a spiral 

•in. Many, however, are less regular in shape 

than any oi those just mentioned. There are also nebulous 

lUTOtinded by more or less nebulous matter ; 

equently seen in most extensive nebulae. 

Tlu oi course, may be at a distance from the nebulae 

in which they appear, either because they are between us and 

the ncbula\ or beyond the nebula?. But it is likely that 

: the stars are really in the nebula? where they appear 

to be. 

££&• One nebula can be seen from the northern parts of 

rth without the help of a telescope; it is in the con- 

acda ; but it looks like a little piece of the 

;:itil it is examined with a telescope. There is 

ilia in the constellation Orion, surrounding a 

ich looks like one star until we see it through 

:>e. The nebula about the star makes it look a little 

hazy, but not hazy enough to attract much attention. The 

. however, shows us this nebula as one of the largest 

and most remarkable objects of its kind. The nebula around 

the 1 ready mentioned (100), is somewhat 

■ 

le clusters of stars are most abundant along the 

ind in what appears to us as its neighborhood, 

nebula? are scarcest in those regions, and abound in certain 

others. The I I present wholly unknown. 

made to determine by means of 
the spectroscope (70. in nebulae are moving 

tem ; but as yet these attempts 
have not 

IM 1 e number of nebula? not large enough or not 

h to be seen from h, but situated within 

.loch our observations extend, 

is proba .red with that of the visible 



132 Outlines of Astronomy. [Sec. 228. 

nebulae. Any object like a nebula which is near enough to 
the Sun to be considered as belonging for a longer or shorter 
time to the Solar System is called a comet ; and several 
comets are usually noticed every year, although few are 
bright enough to be seen without a telescope. Some comets 
move in orbits much like those of the planets, except that 
these orbits are ellipses of considerable eccentricity. Comets 
of this kind are called periodical comets. They are all SO 
faint that they can only be seen when they are near their 
perihelia (146) ; but their whole orbits can be determined from 
the observations made while they are in sight, so that the 
time when they will next be seen can be foretold. But most 
of the comets which are seen are supposed to pass through 
the Solar System only once, and their orbits, while they are 
passing through it, are of the kind called parabolic or hyper- 
bolic. A parabola is an ellipse so eccentric that its length is 
out of all proportion to its width ; and a body moving round 
the Sun in a parabolic orbit would keep on going farther and 
farther away from it, after once passing its perihelion, so that 
it would never reach any place which could be called its 
aphelion (146). A hyperbola is a line like a parabola in 
appearance, but differing still more from an ellipse ; so th.it a 
hyperbolic orbit round the Sun, like one which is parabolic, 
never brings a body moving in it to its aphelion, and accord- 
ingly brings it only once to its perihelion. Now. as none of 
the numerous comets moving in parabolas or hyperbolas are 
likely to have been seen before, we must suppose that small 
nebulous bodies are very abundant in the parts of the uni- 
verse through which the Solar System is passing, and prob- 
ably elsewhere. 

229. Comets appear to shine partly by reflected sunlight, 
like planets, but mainly by light of their own ; for as they 
approach the Sun, the light and heat they receive from it 
make them partially incandescent, or perhaps only phospho- 
rescent. At the same time, part of the solid or liquid matter 
which may belong to them is probably turned into gas. As 
they withdraw from the Sun, they become cooler, and give 



Sec. 229.] Nebuue, Comets, and Meteors. 133 

out less light of their own, while they are also less lighted up 
the Sun. But in this process of heating and cooling, the 
BUItt iich comets consist seems to become scattered, 

aru i r comea together again entirely. Hence a 

xJJcal COl g its perihelion a number of 

t j nv j ther broken up into little bodies, each of 

>und the Sun in an orbit of its own, although the 
Is ■;" all will not differ much from each other. These 
little bodies cannot be seen at all, unless they come very 
se to the Earth ; and hence a periodical comet may appear 
and fainter at each perihelion passage, and 
een turned into a number of me- 
teors (28). We do not know that all meteors are fragments 
of comets ; probably some are, and some are not. 

ftS#, of the action of the Sun upon a larcre 

oat a shining streamer, or perhaps 

m«>re than one ; tl liners are sometimes about as long 

r axis of the Earth's orbit, but usually much 

shorter. They are called tails ; but they are no more likely 

to be behind the main body, or head, of the comet than to be 

before it ; for they are generally turned away from the Sun, 

so that when a comet is moving away from the Sun its tail 

most. The tail of a comet, however, is not always 

turned exactly a y the Sun, and comets have been 

D with short tails pointing towards the Sun. The matter 

of which a comet's tail is formed seems to be thrown out on 

the side I ^un, and then to be thrown back beyond 

the comet on the other side. The tails of comets are usually 

and seem to be hollow. The explana- 

appearances is still unknown : and it 

is part: fffficult to understand, when the tail of a 

pidly half round the Sun about 
the time of the comet's perihelior. , how it can 

kept pointing av 'he Sun. To account for this, 

that the visible part of a comet may 
sometimes be si: 

Me only when the sun! it through the Comet : 



134 Outlines of Astronomy. [Sec. 230. 

so that the tail, on this supposition, would be a sort of lumi- 
nous shadow of the comet. l)ut this explanation has Dot 
proved satisfactory to those who have carefully studied the 
appearances presented by comets ; and we must wait for 
more knowledge than has yet been gained before the various 
questions which may be asked about the tails of comets can 
be settled. 

23IL Not only the tail, but the whole, of almost every 
comet is so transparent that faint stars may easily be seen 
through it; and no comet lias been found to have any mass 
large enough to be noticeable by comparison with the BBS 
of the planets, or even of their satellites. Sometimes comets 
look like nebulous stars ; that is, a comet of this kind I 
sists of a rather bright and seemingly small spot of light, 
called the comet's nucleus, surrounded by a nebulous ap- 
pearance known as its coma, with or without a tail. There 
are also comets which have only a coma, and no nucli 
The coma of a comet is generally a round object, but its form 
changes from time to time. 

232. It is difficult to determine the exact shape of a comet's 
orbit, since we see the comet only while it is passing over a 
part of its orbit which is small compared with that which it 
traverses while it is out of sight. If a comet moves in a \ 
long ellipse, the part of its orbit over which we see it move 
cannot well be distinguished from part of a parabola or hyper- 
bola. It is usual to assume that a comet moves in a para- 
bola, when its course cannot be exactly made out ; so that 
some comets may really be periodical which are supposed to 
have parabolic orbits. On the other hand, when the orbit 
of a comet is presumed, from the observations made upon 
the comet, to be a long ellipse, we cannot be very sure that 
the comet will ever reappear. The orbits of some comets 
are much changed, according to known laws of motion, in 
consequence of the approach of these comets to any large 
planet. Thus, for example, a comet which appeared in 1770 
had passed near Jupiter, and in consequence of its situation 
with regard to that planet its orbit had become an ellipse of 



Sec. 232.] Nebuub, Comets, and Meteors. 135 

such a form that the comet could traverse the whole ellipse 

once in five and a half years. But after passing its perihelion 

it returned in its new orbit to the neighborhood of Jupiter, 

where its course was changed a second time, so that it never 

- J, it of the Earth. 

Many comets have retrograde motion ; many, too, 

orbits the planes of which differ greatly from that of 

the ecliptic. But the larger number of comets known to be 

xlical have direct motion in orbits the planes of which 

not differ more than the planes of some planetary orbits 

n the plane ot the ecliptic. Comets are named by the 

js of their appearances or of their perihelion passages ; 

thus, the first comet of 1S43 * s the comet which passed its 

irlier in that year than any other which was 

L Periodical comets are also known by the names 

of the astronomers who either discovered them or showed 

them to be periodical. 

234. The most remarkable of all recorded comets is per- 
first comet of 1843. just mentioned. It was at one 
time bright enough to be seen by day, and its tail was of 
extraordinary length. But in these respects other comets 
nviv have equalled it ; the most wonderful fact in its history 
that at its perihelion the comet was only distant from the 
photosphere of the Sun by about one-fourteenth of the Sun's 
diameter. It therefore went through the atmosphere of the 
Sun. its speed being at that time so great that it occupied only 
two hours in ^oin^ half round the Sun, and returning to the 
•hern side of the plane of the ecliptic, on which side its 
\cept that part of it which formed, 
-e round the Sun on the 
northern the plane of the ecliptic. The tail of the 

cor Jy whirled round in the course of a 

couple of ho • one way at the beginning and 

the it the end of this short time. It is almost 

e that the matter forming this tail con- 
tinued to be the same throughout this change. The comet 
of 1S43 mav perhaps be periodical. 



136 Outlines of Astronomy. [Sec. 235. 

235. The sixth comet of 1858, called also Donati's Comet, 
was a conspicuous and beautiful object for several months 
towards the end of that year. It has been thought to be 
periodical. 

236. The second comet of 1861 could not be seen from 
the Earth's northern hemisphere till just after it had passed 
its perihelion, when its long tail was unexpectedly seen about 
the end of June. The Earth is supposed actually to have 
passed through this tail ; but as the tail of a comet doubt! 
consists of something much less dense than our atmospl. 

it is not surprising that no noticeable effect was produced 
upon us by the encounter thus presumed to have occurred. 

237. The first comet found to be certainly periodical is 
that called Halley's Comet. It appears about four ti 
every three centuries, and was last visible in 1836. It will 
again be in sight about 191 2. It .seems to have been a \ 
large and bright comet several centuries ago, and on more 
recent occasions it has appeared with a tail of considerable 
length. 

238. Encke's Comet goes once round the Sun in about three 
and one-third years. No other comet is known to return 
often as this. It is a faint comet, scarcely to be >een even with 
good telescopes. The time it requires to go round the Sun 
has been slightly but steadily growing less since its discovery. 
This has been thought to be due to the resistance offered to 
the comet by the ether, or by some kind of matter through 
which it may have to pass. It may seem strange to sup: 
that a comet is made to go round the Sun in less time than 
before by being hindered in its movements ; but if its head- 
way were stopped altogether, it would fall into the Sun ; and 
if its headway is lessened, it will fall in a little towards the 
Sun, so that its orbit will be closer to the Sun, and therefore 
shorter, than it was before. This shortening of its orbit will 
make its speed greater, according to Kepler's third law; so 
that there will be two reasons why it should come round 
more frequently than at first to any part of its orbit. First, 
it has less distance to go; and secondly, its speed is in- 



Sec. 23S.] Nebuub, Comets, and Meteors. 137 

creased. These reasons will be more than enough to pre- 

I it from being delayed in its return to its perihelion, tor 

any resistance made to its movement by the 

ertain that this is the right explanation 
of the peculiar m - of Encke's Comet, which are still 

aomers. 

E I formerly went round the Sun once in 
about six and a half years ; it was scarcely ever to be seen 
scope. Its orbit nearly crosses that of the Earth ; 
so that half a century ago it was shown that it would probably 
come into contact with the Earth sooner or later, as its orbit 
Jd be likely to change enough to bring it occasionally 
very dose to the Earth's orbit, and as the Earth, on some 
ision of the k issing along that part of its 

orbit which the comet was crossing. Biela's Comet, when 
D in 1S46. was found to have separated into two comets. 
These two l I ;>peared in 1852. but they were not seen 

looked for in 1059 or 1S66. Before 1872, 
had learned that some at least of the objects 
called shooting stars might be considered as little fragments 
of the matter like that which composed some comets. It 
rod by calculation that the orbit of Biela's Comet 
ght have been changed enough, since the comet had been 
seen, to bring - the end of 1872 ; so 

n numcr n on the evening 

■ 1S72, it was thought that they might belong 
omet. the matter of which was supposed to have 
become so muc: ! no longer to be visible at any 

cor mce in the shape of a comet. On this sup- 

id from the northern to the southern 
side of the plane of the ecliptic about the time when the 

inch a way that it would after- 
I from the northern parts of the Earth ; 
1 the courses taken b) 
it to judj eabouts in the southern sky the comet 

!d l>e seen, - . it to be visible at all. I 

.gen, in Germany, immediately sent to 



138 Outlines of Astronomy. [Sec. 239. 

Madras by telegraph the information required in order that 
the comet might be looked tor ; and something having the 
appearance of a comet was actually seen at Madras near the 
place where it was thought that Biela's Comet might be. 
Cloudy weather, however, made it impossible to get observa- 
tions enough of this object to determine whether it was really 
Biela's Comet or not. But it seems likely, at all events, that 
Biela's Comet is now nothing but a swarm of meti 

240. Other periodical comets, too, are thought to be 
mainly or wholly clouds of the little objects to which the 
name of meteors is now usually given. As a comet of this 
kind breaks up, the meteors belonging to it are scattered, in 
the course of years, all along the neighborhood of the comet's 
original orbit ; for though each meteor goes round the Sun 
as before, all of them do not go equally fast Thus, by 
degrees, the comet may be turned into a sort of ring sur- 
rounding the Sun and revolving about it. We know that 
there are many rings of this kind, whether they have fo 
formed from comets or not. The meteors which comi>ose 
them are in most places not near enough to each other to 
appear even like a faint cloud in our telescopes, although that 
appearance may be shown by the part of a meteoric r 
where the meteors are most crowded ; and then the cloud 
which is seen may be called a comet. When meteors come 
into the Earth's atmosphere in the course of their mo 
ments, they are made so hot by their quick motion through it 
that they become incandescent and appear like moving sparks, 
which we call shooting stars. 

241. Accordingly, if the Earth could be kept at any one 
of a great number of places in its orbit, a constant stream of 
meteors would be moving past it. If the Earth were deep in 
the midst of this stream, great numbers of shooting stars 
would be continually appearing on that side of the Earth 
turned towards the approaching meteors. But if the Earth 
were only just within the stream, where the meteors would 
probably be farther apart from each other, the shooting stars 
would be less abundant. Streams of this kind are supposed 



Sec. 241.] Nep.ul.f., Comets, and Meteors. 139 

to be often very wide and deep in comparison with the size 
the Earth, SO that while some meteors are crossing the 
:. other meteors belonging to the same stream 
v it at a distance from it of many thousands of 
mi! 1 stream of meteors, especially if its course 

slants g that ot the Earth, may take in so much of the 

Earth's orbit as to show us many shooting stars for several 
nights in succession. Every year, as the Earth comes to 
ices where its orbit is crossed by streams of meteors, 
Stars belonging to those streams. Over one 
hundred streams o( meteors are thought to cross the Earth's 
orbit ; and it is likely, therefore, that thousands of similar 
ire constantly moving round the Sun. As 
rally long ellipses, their perihelia must 
be somewhat crowded together in the region near the Sun, 
le the m of their orbits point every way from the 

Sun, so that their aphelia are far apart. It is likely, then, 
that meteors .ire at all times more numerous in the neighbor- 
Sun, and perhaps in the neighborhood of any 
cat distance from it. 
Only two of the streams of meteors crossed yearly by 
the Earth are remarkable enough to be separately mentioned 
here. Each of these streams has a comet belonging to it ; 
but the Earth has never encountered either of these comets, 
so fai known. The August meteors, as they are often 

called, form a ring which crosses that part of the Earth's 
orbit which • early in August. The orbits of 

:v inclined to the plane of the 
ecliptic, so that each meteor moves with respect to this plane 

ream thrown by a fire- 

the window of a house into 

Which tl. town, when the pipe is held about on a 

; With the In this ball dropped from the 

;:e upon the stream would go 

I heavy to be carried 

r. Hut if the Stream is sent into a window 

Which it conies, the path of a ball 



140 Outlines of Astronomy. [Sec. 242. 

dropped from the top of the window- frame upon the stream 
will slant across it, and the ball will be comparatively 1 
going through the stream. Now, although the courses of 
the Earth and of the August meteors are such as to resemble 
those of the ball and the water in the first of these two exam- 
ples, the Earth is several days among the meteors. The 
meteors of this stream are rather evenly distributed along it, 
so that many shooting stars are seen every year early in 
August, being usually most abundant on the evening of 
August 10. These shooting stars seem to move every way 
from a part of the sky in the constellation Perseos 
appearance due to the effect of perspective, as will be shown 
hereafter. 

243 The other stream of meteors to be mentioned here can 
hardly be said to form a ring, because most of the meteors 
belonging to it are collected in the neighborhood of the comet 
which belongs to the same stream, so as to leave but few 
about other parts of this comet's orbit than that along which 
it happens to be moving. These meteors and their comet 
have their aphelia near the orbit of Uranus, and their peri- 
helia about that part of the Earth's orbit where we arrive in 
the middle of November. They travel once over the whole 
course of their orbits in about thirty-three and one-fourth 
years, and the part of the stream where the meteors abound 
reaches about one-eleventh part of the way round the! 
bits, so that it takes about three years for this crowded part 
of the stream to pass any particular place. Accordingly, a 
great many shooting stars are seen from November 13 to 
November 15, for a few years at a time, and then only a small 
number each year at the same time for thirty years or so, until 
the crowded part of the stream comes to its perihelion pas- 
sage again. The orbits of these meteors are not greatly 
inclined to the plane of the ecliptic, and their movement is 
retrograde, so that the Earth moves against the stream 
of meteors while passing through it. When any of these 
meteors appear as shooting stars, they seem to move every 
way from a part of the sky in the constellation Leo. They 






Sec. 243.] Nebula, Comets, and Meteors. 141 

were 1 lenty in 1866, 1867, and 1S6S ; so that probably few of 
them will be seen till about the end of the nineteenth century. 
244 s the meteors belonging to rings or streams, 

Ifbi .led periodical meteors, there are others, called 

sporadic meteors, which are not known to belong to any par- 
ticular meteoric swarm. Shooting stars are to be seen at 
all I ; and some of the meteors (whether they are 

periodical or 5 . which enter the Earth's atmosphere, 

compact that they make their way through 
>me to the ground. It may seem as if the air 
• it >p any but very light meteors ; but, in fact, a body 
moving many miles a second through even the thinnest air is 
•1 burned up if it can be set on fire, and if not, then 
crumbled to dust, by the heat produced in it by the resist- 
e of the air to If it were not for the air, we 

aid be in constant danger of being struck by meteors ; 
but . accidents of this kind are very rare, and it is 

iom that a meteor is known to reach the land or sea. 
Ho lumps of stone and metal are sometimes 

found where a lar^e and bright meteor has come down. 
These lum;)s are usually called aerolites ; they occasionally 
ral hundred pounds. Some of them contain a 
it deal of iron. None have been found to contain any 
Iso found in terrestrial objects ; but their 
: sometin ined chemically in ways which 

differ somewhat from those in which terrestrial minerals are 

g is has been found in 
an aerolite, alone: with iron, the quantity of this hydrogen 
beinjj sufficient the supposition that the 

aerolite had been formed un<: re, and where 

1 that the iron became strongly 
cha This has been thought to show that 

> arc produced by eruj ie Sun and other 

n are likely to be 

nination of aerolites with the 

microscope has ^ \ like kind. But 

ill very uncertain. 



142 Outlines of Astronomy. [Sec. 245. 

245. Aerolites usually first appear as large luminous ob- 
jects, like shooting stars much larger than usual, — un;> 

as frequently happens, they fall by clay ; before reaching 
the ground they often explode with a loud noise, and their 
fragments are scattered over a considerable space, 
occurrence of this kind was observed in June, 1866, in the 
north-eastern part of Hungary. A meteoric stone fell near 
Searsmont, Maine, in May, 1S71. 

246. Sometimes a large bright meteor is seen passing, 
which does not appear to come to the ground, or to explode. 
A meteor of this kind is often called a fire-ball. These 
meteors probably crumble to dust, like little shooting stars, 
before reaching the ground. 

247. Bright shooting stirs, and large meteors, often leave 
trains of little sparks behind them. These trains sometimes 
remain in view for many minutes after the appearance of the 
meteor. 

248. The Earth, and other large objects, must be slowly 
increasing in size from the constant addition of meteoric dust 
and of aerolites. However, it would probably require thou- 
sands of years to add an inch in this manner to the Earth's 
thickness. 

249. It has been thought that the heat produced in the air 
by the passage of meteors may be enough, or more than 
enough, to make up for the heat sent out by the Earth. But 
this seems to be only a guess, and geologists generally con- 
sider that there is reason to regard the Earth as a body grad- 
ually growing cooler. 

250. The height at which meteors are seen, as determined 
by observations taken at different places about the same time, 
is occasionally over a hundred miles. Hence we conclude 
that the Earth's atmosphere extends at least to that distance. 
It is not likely that many meteors which have once entered 
the air pass out of it again. If any do so, their orbits must 
usually be so much changed by the resistance of the air to 
their movements, that if they were previously periodical, they 
are afterwards sporadic meteors. 



Sec. 251.] Phenomena. 143 



CHAPTER VII. 

PHENOMENA. 

ML In the preceding chapters, the attempt has been made 
to state the most important tacts as yet discovered with 
id to the material universe and the different kinds of 
which compose it. We can now go on to the expla- 
nation, by means of these facts, oi various appearances which 
ind and beyond the Earth. 
feft£« W prill first consider exactly what we mean by the 
I down. If a heavy object of any kind is fastened 
rd, and hangs by this cord, without 
lid object ; then, as every one knows, 
part of the cord will be straightened out by the weight of the 
and when it has ceased to move, this 
;>art of the cord will reach upwards from the hanging 
towards it. A line which thus reaches 
is a vertical line. 
£53. If the Earth were an exact sphere of the same 
density in all p v vertical line would point down- 

war the centre of the Earth (157), and upwards 

m that centre. But owing to the spheroidal 
D of the I j ;>. as well as to its roughness and to the 

dirT» in different parts of it, vertical lines do 

illy point re. However, they point 

re. to allow us to consider them as 
Hsfa to speak accurately. 
iown may ac< lined as meaning 

're ; and the word up as meaning 
away from t The words op and down, 

wh. ide the Earth, have different 

the North Star M nearly 



144 Outlines of Astronomy. [Sec. 253. 

Above the Earth's north pole, it is nearly below the Earth's 
south pole. Of two men on opposite sides of the Earth, 
each is below the other, in the ordinary sense of the word 
below. 

2.54, The words up and down, and others like them, are 
sometimes used in speaking of other bodies than the Earth. 
Thus, the Sun's chromosphere may be said to be above its 
photosphere, because it is farther from the Sun's centre ; and 
an aerolite (244) which strikes any other planet than the 
Earth may be said to come down towards that planet before 
striking it. In one sense, the Sun may be said to be al\\ 
below the Earth, because the Earth has a real falling m< 
ment towards the Sun ; hut it would be of no use to employ 
the word below in this manner. It is usually best to 1 
sider the word up as meaning only along a straight line from 
the Earth's centre through the place of something in 
to which the word is used ; and to consider the word down 
as meaning only along a straight line from the place of some- 
thing in regard to which the word is used through the Earth's 
centre. An object is in the zenith of any place when it is 
exactly over that place, and in the nadir of the same place 
when exactly below it. 

25-> Suppose a vertical line to be the axis of a rotating 
globe ; then all parts of the equator of that globe will be on 
the same level; and the plane (137) in which this equator 
lies will be a level plane, or, as it may also be called, a hori- 
zontal plane ; it will pass through the centre of the supp 
globe, which may be anvwhere we please in the vertical line. 
Every line lying wholly in this plane will be a horizontal 
line, and all its parts will be on the same level. The \\ 
horizon is in common use with the meaning of the ring where 
the sky, as seen from any terrestrial place, seems to meet the 
Earth. In its ordinary sense, the horizon is not usually 
horizontal, on account of the Earth's roughness ; but if we 
have still water all around us as far as we can see, our hori- 
zon will be a horizontal line. But it will not be on the same 
level with the top of the water near us. If a raft could be 




Sec. 255] Phenomena. 145 

made so large as to be some miles across, and yet perfectly 
>uld be above the water which supported it : 
th is not flat, but round. Accordingly, when the 
. water is observed with suitable instru- 
>und to dip. according to the usual phrase ; or, 
ther words below the Level of the place from which 

it is obs fact that the horizon is always ring- 

shaj>ed is sometimes called a proof that the Earth is round; 
but if the Earth were rlat, we could see no farther one way 
thai that our horizon would still be a ring. But 

in t lild be no such dip of the horizon as we 

illy find. 
BM, rom what has been said that no two places 

equally far from the Earth's centre can be on the same level, 
in t mat expression. Sometimes, how- 

. el in another sense; as when we 
meaning the distance from the Earth's 
centre of irticular part of the ocean. But the differ- 

ent me.. the words up. down, above, below, beneath, 

of any words, will not puzzle us if we take 
en we use any word, to know just what we mean 

M7< Suppose a high ground to stand between 

two others, one to the , the other to the west of it, all 

three ridges being equally high ; or. in other words, reaching 
equ th'a centre. Then the tops of the 

tern ridges will be below the level of the top 
of the middl ; hence the eastern and western ridges 

will be out of sight of each other. It is (rue that the top of 
the middle ridge lie level of the top of either of 

the . re< kon ; but if we reckon 

le, the top of the western 
r than that of the middle ridge as to be 
it. 
858. In like manner, any terrestrial object which is mov- 

IOW the horizon while it is 
still plainly seen if our view of it 

! 3 



146 Outlines of Astronomy. [Sec. 258. 

were not cut off by the Earth. A traveller, as he approaches 
a range of lofty mountains, may first see their highest peaks, 
apparently resting upon the plain before him. As he goes 
on, lower but larger parts of the range come into sight 
These he could have seen as soon as the higher mount 
tops, if they had not been below the level of part of the plain 
between him and them. Facts of this kind, like the dip of 
the horizon, make us aware of the globular form of the Earth. 
But to determine the Earth's exact shape, careful observa- 
tions with delicate instruments are required. By such obser- 
vations the relative position of horizontal planes in various 
parts of the Earth has been ascertained ; and the form of the 
Earth has thus become much better known than it would be 
if we were placed at such a distance from it as to see at a 
glance that it is round : for then we could oat measure it as 
accurately as we can by our actual surveys of its different 
parts. 

!2.>9. The arched or vaulted appearance above us which 
we call the sky illustrates what has just been mentioned 
(255) with regard to the horizon. We have no means of 
judging how far we can see into the space around us ; and 
accordingly we suppose ourselves, when we look away from 
the Earth, to see about as far one another. Hence 

we seem to be enclosed in somewhat such a hollow shell as 
was formerly called a crystal sphere (128) ; the color of 
which depends on the kind of light reflected to us (8) by the 
air and whatever may be floating in it. If no such light as 
this were reflected to us, the sky would appear black : and in 
fact it seems unusually dark when viewed from great heights 
upon mountains or in balloons, where the observer has much 
less air above him than he has at the sea level. As the 
proportions with respect to each other of the different kinds 
of matter in the air of any particular place are not always 
the same, the color of the sky changes more or less from 
time to time, even while it continues on the whole to appear 
blue : and when it is evenly clouded over it looks gray. We 
do not commonly notice that this gray light comes to us in 



259] Phenomena. 147 

mo- om something within a few miles of the ground, 

while th Here from which we receive the blue light 

led the color of the sky extends to a much greater dis- 

I1S than that o( ordinary clouds ; and the gray 

clou to be in the ordinary form of what we call the 

. since we usually know nothing of the comparative dis- 

I at parts from us. 

MOt We have already seen that besides reflecting light, 

I (51). Hence, if there were no atmosphere 

rou: irth, the Sun and other celestial objects would 

r than they do ; but, on the other hand, we should 

>UT ordinary daylight, which is sunlight 

. by the atmosphere, and diffused, according to the 

ttd ex| . around the various terrestrial objects. Dif- 

when the Sun has lately set, or 
soon before il - called twilight. 

ML Heat, like light, may be absorbed and reflected. It 
would be much less difficult than it is to measure the heat 
reaching the Earth from the stars and from the Moon, if the 
atmosphere did not absorb much of this heat, especially that 
of the Moon (192), which is not an incandescent body like 
the s 

MS, I ght ifl refracted, as well as reflected and absorbed, 

hv the air. A familiar instance of the effect called refraction 

the broken appearance of a stick held slanting and partly 

under still water. The part of the stick under water seems 

to slope more away from a vertical line than the part above 

water. This is because the light which comes through the 

water in any other course than a vertical one is turned still 

irse when it passes from the water 

ie air. a slanting course through 

the the other hand, is turned into a course more 

tl when it enters a level piece of water. \ 
the <>f Bghf coming to it from the o un- 

it much in the same w i\ 

from the air. As 
■ carer the Earth, the air through which 



148 Outlines of Astronomy. [Sec. 262. 

it passes continually increases in density and makes its 
course more and more nearly vertical. The consequence of 
this is that any thing at a considerable distance from the 
Earth seems to us a little nearer the zenith (254) than it 
really is. If it is already in the zenith, its place does not 
seem changed ; and the effect of refraction on any thing 
which seems high in the sky is too small to he perceived 
except by accurate observations. But the farther any thing 
from the zenith of any observer, the greater is the change in 
his view of it which the atmosphere produces by refracting 
the light it sends to him. 

2G3. We usually continue to see the Sun on a clear even- 
ing for some little time after it is really below our horizon ; 
for the air, by refracting the sunlight, enables us to look a 
little over the edge of the horizon, so to speak. We also 
the Sun rise sooner than we should if there were no air to 
refract Jts light to us. Other celestial bodies, of course, are 
also actually kept in view longer than they would be if there 
were no air. Hence the Earth may in fact be exactly between 
two stars, one of which has risen before the other has 
So, too, the Moon may rise before sunset, while yet the Karth 
is between the Sun and Moon, so that the Moon appears 
darkened by the shadow of the Karth. Refraction does more 
than the dip of the horizon (255) to widen the prospect around 
the Earth which can he had from ordinary terrestrial stations ; 
but neither of these effects greatly changes the apparent dis- 
tance of celestial objects from the horizon. The light coming 
from terrestrial objects on the sea level to an observer above 
that level passes through air continually lessening in density, 
and its course thus becomes more nearly horizontal as it goes 
on. Hence refraction lessens the dip of the horizon at sea, 
but lessens it very slightly. 

204* It appears from what has just been said that unless 
an object is near the Earth it will always be in sight of one 
or the other of any two opposite places on the Earth, and may 
be in sight of both at once. If two men stand on opposite 
sides of a house, close to its walls, a carriage driven past the 



Sec. 264.] Phenomena. 149 

end of the house may be out of sight of both men while it is 
Strip ot ground nearly as wide as the house. In 
the same way, it' it were not tor retraction, the Moon might 
for three or tour minutes (for a longer time if the Earth's 
rotation were stopped) remain out of sight of both one and 
the other of two places on opposite sides of the Earth, where 
the view was not hindered by hills or otherwise. But this 
could not happen with the Sun, or with any other globe larger 
than the Earth : such an object would begin to rise on one of 
the places of observation before it had set on the other. The 
stars are too far off to show us any disks (80) ; but many of 
them are probably much larger than the Sun ; so that a ring 
which could all be seen at once from opposite terres- 
trial places would not take up a strip of sky having any 
noticeable width. Hence we may say that from any two 
opposite places on the Earth, an outlook towards all distant 
parts of the universe might be had at any given moment 
even without the help of refraction, or of the dip of the 
horizon. With these aids, the views obtained from opposite 
a of the Earth partly overlap each other at a distance 
from the Earth about once and a half as great as that of the 
■ n ; but its exact amount at any particular time depends 
on the state of the atmosphere. A small object, then, as far 
rth as the Moon is, may be at a given time below 
the horizons of two places on opposite sides of the Earth ; 
but all the celestial objects usually seen from any part of the 
Earth must always be above the horizon of one of these 
places or the other ; and some of them may be in view from 
both at once. If we regard the straight line joining the two 
places ;. tical line, the horizontal plane (255) which 

v then be consider- g through the centre of the 

it is sometimes called the plane of the rational 
The view from either p] 
shown, through the plant 

.nee from the Earth ; and 

tfl on the lower side of that 

pla: ail on its upper side, will be above the actual 



150 Outlines of Astronomy. [Sec. 264, 

horizon. Accordingly, those stars which are in the zenith of 
either pole of the Earth are a little above the horizon of any 
part of its equator. 

265. The absorption of fight by the air near the Earth 
prevents us from seeing faint objects which appear to 1 e low 
in the sky, and makes bright objects comparatively dim near 
the times of their rising or setting (51). The atmospheric 
disturbances which make the stars twinkle (106) and inter- 
fere in various ways with accurate observations of them, are 
also greatest along the horizon ; so that a celestial object 
cannot be observed for astronomical purposes at the same 
time from exactly opposite terrestrial stations, as might be 
supposed from the explanation above. The effect of refrac- 
tion increases so fast as we look lower, that the disks of the 
Sun and Moon, when rising or setting, often look oval instead 
of round ; their Upper limbs being less refracted than their 
lower limbs. Sometimes, too, these disks are curiously dis- 
torted by atmospheric disturbance. The reddish tint which 
they occasionally have is an effect of absorption. 

2G6. We have already had several occasions to remind 
ourselves of the well-known fact that objects look smaller and 
closer to each other the farther they are from us. What are 
called effects of perspective depend upon this fact, and celes- 
tial perspective, or the perspective of objects seen in the sky, 
occasions appearances which require some explanation. 

267. Most people have noticed, in crossing some long 
straight railroad track, that the lines of rail seem to slant 
towards each other in the distance, whichever way the s; 
tator may look. In the same way, a number of long straight 
rows of small clouds, such as we sometimes see reaching 
across the sky side by side, seem farthest apart overhead, or 
wherever they come nearest to us, and slant towards each 
other as they approach the horizon on one side of us or the 
other. This slanting is generally only an effect of per- 
spective ; the rows of clouds, like the lines of rail just men- 
tioned, are as far apart at one place as at another ; but the 
distance between any two of them looks less the farther they 



Sec. 267.] Phenomena. 151 

are from us. People not used to drawing are apt not to 

notice effects o\ perspective in objects near them. If they 

.1 one end of a room, lor instance, they do not notice that 

the tioor looks narrower at the farther end of the room than 

at the end where they are sitting ; but others, who have been 

made to tike notice of such facts by the careful practice of 

drawing, or in other ways, see the slant of the edges of the 

Mn as plainly as they see the slant of long lines 

of rail or of long rows of clouds. In the same way, a person 

who takes little notice of what he sees will sometimes say 

that the plate before him. as he sits at dinner, looks no larger 

to him than a plate of the same size on the other side of the 

table. This is only because he knows the plate nearest him 

to be actually no larger than the other, and pays no attention 

to what his eyes tell him. For this reason, people tell us that 

the Sun and Moon look to them as large as wheels, or plates, 

or other terrestrial objects ; and it is often hard to make such 

people understand that a large wheel at a moderate distance 

from them looks smaller than a small plate close at hand. 

Every one will admit, however, that the Sun and Moon look 

about of the same size. Now the diameter of the Moon, as 

we have seen, is about one-fourth of that of the Earth, and 

the diameter of the Earth less than one-hundredth of the 

Sun's diameter : so that four hundred globes like the Moon 

it be put side by side, to reach from one side of the Sun 

In this case, then, the comparative distance of 

lifTerence in their comparative size, 

as judged by the > does the comparative distance of 

two obj- small, and however near us they 

x inches across is three feet from the 

IS IS six feet from the same eye, 

>th plates is the same; as will 

be evident if the nth the two plates. It is 

then, to s.iv that the Moon looks ,s a 

rid 

to B e with each other is to find the 

which awhecl^ind a plate of the 



152 Outlines of Astronomy. [Sec. 267. 

kinds meant to be used in the comparison must be placed in 
order only just to hide the Moon. If an experiment of this 
kind is tried, it will probably be found that the Moon or the 
Sun looks much smaller than was previously supposed. It may 
be worth while to add that doubling the distance of an object 
does not make its apparent width twice as small as before. 
This may seem to contradict what has been said above ; but 
is really consistent with it, as is shown by geometry. 

208. The reason why men commonly judge of the per- 
spective and the apparent size of objects near them in one 
way, and of the perspective and apparent size of distant 
objects in another way, is that they have better means of 
learning the actual size and shape of objects near at hand 
than of others. The view obtained by one eve of the objects 
close at hand differs from that obtained by the Other; so that 
even if the spectator does not move, the comparison of th< 
two views, which is made too often and too quickly to be 
noticed, helps him to learn something of the objtt 
But when we move about, so as to get a variety of views of 
objects near us, and still more when we handle and measure 
them, we learn so much more of their real size and shape 
than we can by merely looking at them from one place, that 
we forget how they look. The sight of them then reminds 
us of certain facts about them, which we incorrectly sup: 
ourselves to see. Distant objects, on the other hand, are not 
seen as they are, but as they look ; because we cannot even 
get different views of them without moving so far that we 
partly forget the first view before we have another consider- 
ably differing from it. In learning to draw, as has been - 
we have to recover our power of seeing how objects look 
when thev are near us. 

269. One way of studying perspective is to look through 
apiece of glass at the objects beyond it and to mark down 
their outlines on the glass. In doing this, the head must be 
kept from moving, and only one eye used ; for it will be found 
that the two eyes see different pictures. The drawing will 
represent the objects as they appear against the glass ; and 



Sec. 269.] Phenomena. 153 

such a drawing may be called their projection upon the 
glass. Objects may be projected in various ways upon other 
objects ; but pictures are not apt to be exactly like copies of 
single projections of any kind ; they are more often like 
copies of a number of separate bits of projections, and are 
more natural for being so, since we do not stand perfectly still 
while we are viewing a real landscape or a real group of peo- 
ple. But in looking at objects so far from us that we cannot 
alter their appearance noticeably by our own movements, 
what we always actually see is exactly like a projection of the 
objects we look at ; this projection being made on any thing 
sufficiently far from us to prevent the disturbance of the pro- 
jection by our movements. The projection may be supposed 
to be either between us and the projected objects, as if it 
were drawn on .something transparent; or beyond the objects, 
just . which is one kind of projection, is farther 

a the light which occasions the shadow than from the 
object which throws it. 

'^70. The projection of one object on another, as appears 
from what has been said, is the shape traced out on that other 
object by a straight line fastened at one end and moved 
round the projected object so as always just to touch it. If 
the fixed end of the line (which is called the point of sight) 
to be farther away from the objects than any 
place which can be named, the projection is orthographic. 
hie projection is a projection of a hemisphere, 
or of a part of it, 00 the plane by which that hemisphere is 
sej m the other, while the point of sight is in the 

die of the outside of that other hemisphere These pro- 
bers, made on the same general prin- 
c i i > . .wing maps. Celestial objects appear to 

j all at the same distance, since we cannot tell their 
v looking at them : so that they appear like 
their own pr<»jr q the imaginary object called the 

I is likewise often true of distant terrestrial 

Objects. When any object which we consider as projected 
on the sky moves directly towards us or directly away from 



154 Outlines of Astronomy. [Sec. 270. 

us, we cannot see by merely looking at it that it moves at all ; 
in other words, the place of its projection on the sky does not 
change, though the projection grows larger or smaller as the 
object approaches or retires. If it moves in some other way, 
its projection on the sky will change place ; in other words, 
it will seem to move ; but this seeming movement will not be 
the same with any real movement which it may have. Sup- 
pose, for instance, that several small clouds pass overhead, 
moving straight forward and keeping their places with re- 
spect to each other. Their projections on the sky will rise 
from the horizon, or from somewhere near it, on one side, go 
farther apart from each other as they rise higher, and draw 
together again as. they descend towards the opposite side of 
the horizon. The actually straight courses of the clouds 
must accordingly seem to be arches leaning away from each 
other at their summits, like those seemingly formed by 
straight rows of stationary clouds (2^7). All this may be 
shown more briefly and accurately by the aid of mathematical 
reasoning than in any other way, but perhaps not so plainly 
as in the way which has here been taken. 

271. Sunbeams shining through openings among clouds, 
and made visible by their effect in lighting up the vapor or 
other contents of the atmosphere through which they pass, 
seem to spread apart more and more the farther they extend. 
This is of course an effect of perspective When this appear- 
ance is seen, the Sun is sometimes said to be drawing water ; 
an expression without much meaning, since water is obvi- 
ously more likely to evaporate in full sunlight than under 
clouds. Sunbeams are also seen at times to extend from one 
side of the horizon to the other in the form of arches farthest 
apart from each other at their summits, like the rows of 
clouds already mentioned. 

272. A similar effect of perspective appears in the stream- 
ers of the aurora, or northern lights, as the aurora is often 
called in the northern hemisphere, where it appears oftener 
in the northern sky than elsewhere. The auroral streamers 
of the northern hemisphere, when they are of a considerable 



Sec. 272.] Phenomena. 155 

length, seem to spread apart for some distance from the 
northern horizon, and then begin to close together again, all 
pointing to a place somewhat south of the zenith. We con- 
clude from this appearance that the streamers on the whole 
are straight, and as far apart in one part of their course as in 
another. They point the same way with a magnetic needle 
which has come to rest after being balanced, so that it can 
turn freely not only sideways, but also with a tilting or dip- 
ping movement. This circumstance, as well as others, shows 
that the auroral light is in some way due to magnetic or elec- 
tric action ; but its nature is still little known. One interest- 
ing theory, which seems now to be generally admitted, is 
that the disturbances on the Sun, which manifest themselves 
to us bv the formation of spots and protuberances, occasion 
sturbances on the Earth, which result in auroras 
and peculiar movements of the magnetic needle ; so that 
rial appearances become more frequent with the 
increase in frequency of the solar spots, and become less fre- 
quent as the number of solar spots decreases. Auroral dis- 
plays, for instance, were frequent and brilliant, sometimes 
extending all over the sky, about the years i860 and 1870; 
the light seen on these occasions being often of various 
Jn colors, especially red, yellow, and green, instead of the 
greenish white of ordinary auroral light. Maxima of solar 
spots also occurred in i860 and 1870 (63). It is likely that 
some of the appearances which, taken together, make up 
call the weather, are also periodical, and that their 
aency cl. h that of the solar spots ; but nothing 

yet been learned on this subject. The light 
clouds which have a hairy appearance and are called cirri 
have been th r instance, to be in some way connected 

with auroras, and to change with them in frequency. 

n J. When auroral streamers appear over a large part of 

the sky at once, their upper ends generally seem to be bent 

•<> form a ring (called a corona) round that 

par* iky towards which they point for the greater part 

of their courses. They sometimes remain Steady for a time 



156 Outlines of Astronomy. [Sec. 273. 

and at other times change rapidly ; and especially towards 
the end of an auroral display, flashes of light seem to shoot 
upwards along them. In ordinary auroras, the light is often 
mainly in the form of an arch with dark sky below it. When 
such arches are seen in the northern hemisphere, they appear 
in the northern sky. But there are other kinds of auroral 
arches and luminous belts seen occasionally in various parts 
of the sky, the light of which, when examined with the spec- 
troscope, seems to show that they are appearances of a 
decidedly different kind from those of ordinary auroras. 
However, little has yet been discovered about them. The 
height of particular patches of auroral light has sometimes 
been estimated by means of observations made at the same 
time in different places. According to these estimates, some 
auroral light may be as much as five hundred miles above the 
sea level. If we suppose it to be occasioned by electrical 
discharges through gas of little density, we shall probably 
infer that there are gases in the Earth's atmosphere BO light 
as to extend five hundred miles from the land and sea (174). 
On this estimate of the height of auroral light it is plain that 
a patch of it cannot be seen from places on the Earth oppo- 
site or nearly opposite each other (264). 

274* Auroras are seen in the southern, as we'll as in 
the northern hemisphere ; and appear there mainly in the 
southern sky. The name aurora originally meant the morn- 
ing twilight, or dawn ; and to distinguish them from this, the 
appearances commonly spoken of at present as auroras are 
sometimes called polar auroras ; the aurora of the north being 
also named aurora borealis, and that of the south aurora 
australis. 

275. The apparent paths of shooting stars illustrate what 
has been said of perspective, as do the sunbeams seen through 
clouds and the auroral streamers. If many meteors, all mov- 
ing nearly the same way, plunge into the Earth's atmosphere 
at places far apart from each other, they will appear as shoot- 
ing stars in different parts of the sky. But if we mark their 
tracks upon a chart, they usually seem to be parts of arches, 



Sec. 275.] Phenomena. 157 

which, when completed, all pretty nearly meet each other at 
two opposite places in the sky. One of these places is on 
the side of the Earth from which the meteors come, and is 
commonly called the radiant point of the meteors. As we 
have seen, the radiant point of the August meteors is in 
s (242), and that of the November meteors in Leo (243). 
The radiant point of the meteors of Biela's comet is in Andro- 
meda, and the place opposite to it. where the comet was looked 
for at Madras {-39), in Centaurus. The constellations serve 
) to point out the part of the sky where any thing is seen. 
% 2 7G. The appearances called halos, parhelia, and the like, 
are effects produced by vapor or by crystals of ice or snow 
j in the air. A halo is a ring of light, sometimes 
colored, and surrounding the Sun or Moon. Halos are 
D seen round the Moon. Small halos are called coronae. 
A parhelion i^or a sundog) is a bright spot looking some- 
thing like the Sun. A similar appearance produced by moon- 
I is called a paraselene. The Sun sometimes appears 
surrounded by an oval ring with a parhelion at each end and 
at each side. 

*^T7. The zodiacal light is a luminous appearance occa- 
sionally seen in the west after sunset or in the east before 
sunrise. It is broadest at the horizon, tapering upwards to a 
point, and lies along the zodiac, which may be described as 
on of the sky occupied by certain constellations 
among which the Sun and Moon seem always to move. The 

reflected from clouds of small 
re these meteors are is not yet settled. 
'27*. The tides of the ocean are generally included amonjr 
astronomical phenomena. They consist of waves of extremely 
• width in proportion to their height There are two 
principal tidd waves, the summits of which are on opposite 
s of the Earth, and move round it regularly with a ste 
ment The disturbance of these 
the land which they encounter here and tl 
number of second ich occasion peri 

cal ( Dg backward and forward about the 



158 Outlines of Astronomy. [Sec. 278. 

of the various continents. When two or more of these cur- 
rents meet in a narrow bay, the tide there rises high and falls 
low ; in other places the tide due to one current may be high 
when that due to another current is low ; and in those places 
the rise and fall of the tide must be small. Differences of 
this kind often make the tides of one place very unlike those 
of another, not only in height, but also in other respects. On 
some shores there is only one tide a day ; on others there are 
two, about equally high ; and on others there are two ti 
but one higher than the other. 

279. What is properly called a tidal wave, then, is a wave 
a few feet in height and many miles across, so that it is too 
low and wide to appear to the eye as a wave at all ; and it is 
also distinguished from other waves by coming back at regu- 
lar times. A foolish habit has arisen, however, of calling 
any large and unexpected wave a tidal wave. This use of 
words is of course mere nonsense, and cannot be excu 
even by the great violence and speed with which the highest 
tides rush into some narrow bays and up some rivers. 

280. The time and height of the tides depends upon the 
piaces of the Moon and Sun with respect to particular parts 
of the Earth, as will appear hereafter. There must be tides 
in the atmosphere, for the same reasons according to which 
there are tides in the ocean ; and the currents of both air and 
ocean which are not tidal are governed largely by the Earth's 
movement of rotation, as the tidal currents are (163). The 
apparent movement of celestial object! which is due to 
the rotation of the Earth has already been partly con- 
sidered (124), and we have now only to see how it differs in 
different terrestrial places. In considering this difference, 
we will pay no attention to any movements of the stars, 
apparent or real, except such as are due to the Earth's rota- 
tion. In fact, all the movements of the stars which are not 
due to the Earth's rotation are either too slow or too small to 
be easily noticed. 

281. To an observer stationed at either pole of the Earth, 
the daily course of any star will seem to be a level ring. The 



Sec. 2S1.] Phenomena. 159 

Earth's axis will point directly upwards and downwards. The 
stars nearly in a line with it will have scarcely any movement, 
so that those which are overhead at one time will also be 
overhead at any other time. If any star is exactly in the 
zenith, it will stay there, so far as its movements depend on 
the Earth's rotation ; and any star which maybe in the nadir 
will remain under the Earth. A star in the zenith of one pole 
must be in the nadir of the other. The stars which seem 
near the horizon of one pole also seem near the horizon of 
the other (264) ; so that their daily courses will be along the 
horizon of either of the poles. The higher a star seems in 
the sky, the smaller will be the ring in which it seems to 
move ; but one part of this ring will seem to be on the same 
level with any other part of it. Under these circumstances, 
there can be no eastern or western part of the horizon (156). 
All parts of the horizon of the north pole are in the south, 
and all parts of the horizon of the south pole are in the 
north. 

»Jh\>. But if a traveller should set out from either of the 
poles, and move away from it as directly as he could upon the 
Earth, he would find, as soon as he had gone far enough to 
notice the change in his level, that the daily courses of the 
stars were sloping downwards behind him and upwards before 
him. The stars which at first moved along the horizon would 
now be above the horizon for that half of their courses in front 
of the traveller and would be below the horizon for the other 
half; so that they would rise on one side and set on the other. 
The part of the horizon where they rose could now be called 
the eastern and that where they set the western part. If 
the traveller should now turn so as to face the eastern part 
of the horizon he would have the north on his left and the 
ttb on his right This is another way of distinguishing 
between north and south, besides that already mentioned 

MSi the traveller continues his journey directly south- 
war the case may be. he will everywhere 
find that those stars which at first moved along the horizon 



160 Outlines of Astronomy. [Sec. 283. 

now rise in the east and set in the west. This amount 
saying that his journey changes his view of the stars in no 
other way than that in which he might change it (if the Earth 
were transparent), by simply leaning forward. As he goes on, 
each star which rises in the east daily stands higher in the sky 
half-way between its rising and setting, until at length it pas- 
ses directly over his head. He is now on the equator ; and 
the stars which were at first nearly in his zenith and nadir are 
now near the horizon behind and before him. If he goes on, 
the stars which were at first nearly over his head sink under 
the horizon behind him and those opposite stand higher and 
higher until they are over his head. He has now reached the 
pole opposite to that from which he started. 

£8-1. The stars which rise and set everywhere on the 
Earth except at places close to its poles, which always rise 
nearly due east and set nearly due west, and which are alu 
nearly above one part or another of the equator, may be called 
equatorial stars. Their daily courses appear to be larger 
rings than those in which any other stars move, and lie along 
the horizon of either of the poles. The stars nearly in the 
zenith of either of the poles may be called circumpolar st 
all stars appearing at the north pole to be higher in the sky 
than the equatorial stars may be called northern stars ; and 
all appearing at the south pole to be higher than the equatorial 
stars may be called southern stars. 

£8»>. At any place north of the equator more than half the 
daily course of each of the northern stars is above the horizon ; 
some of these do not set at all (124) ; and the rest rise nortfc 
of east and set north of west. More than half of the daily 
course of each of the southern stars is below the horizon ; 
some of them do not rise at all ; and the rest rise south of 
east and set south of west. To describe the appearance of 
the stars from any place south of the equator, we have only, 
in the last two sentences, to exchange the words north and 
northern for south and southern, and the words south 
and southern for north and northern. At the equator, the 
courses of all the stars seem to be upright arches, about 



Sec. 285.] Phenomena. 161 

half the course of each star being above the horizon. The 
equatorial stars pass overhead, while both the northern and 
the southern circumpolar stars come into sight, although they 
are never tar above the northern and southern parts of the 
horizon (204.). 

*JM>. The Sun, in consequence of the Earth's yearly 
revolution round it, has not always the same apparent daily 
movement ; it is in fact sometimes one of the northern and 
sometimes one of the southern stars, being an equatorial star 
whenever it is passing through the zenith of any place on the 
equator. If the equator lay in the plane of the ecliptic, the 
Sun would always be an equatorial star. For then the Earth's 
centre would always lie in the plane of the ecliptic, inside the 
ring formed by the equator ; so that the line from the centre 
of the Earth to the centre of the Sun must always cross the 
equator at one place or another, through the zenith of which 
the Sun would be passing at the time when the line was sup- 
posed to be drawn. 

v***7 We will begin by supposing the Sun to be always an 
equatorial star. In that case, the movement of the Earth in 
its orbit will be westwards from that place on the equator 
which is at any time beneath the Sun. This westward move- 
ment of the Earth will give the Sun an apparent eastward 
movement, only quick enough, however, to carry it round the 
place of observation once a year. Meanwhile, the rotation of 
the Earth will be giving the Sun an apparent westward move- 
ment, so quick as to carry it round the place of observation 
once a day. On the whole, then, the Sun's apparent move- 
ment will be rd, but not quite as quick as it would be 
if the Earth's movement in its orbit were stopped and only 

Mss, A- •' • -. the apparent movement of the 

Sun will carry it towards the western horizon. Meanwhile, 
the inging the place of observation 

Dg which the Earth's centre is 
carried round the Sun. At sunset, therefore, the Earth's 
movement in its orbit has become nearly a downward move- 

1 1 



1 62 Outlines of Astronomy. [Sec. 288. 

ment, so far as the place of observation is concerned. The 
Sun's apparent movement due to the Earth's movement in its 
orbit is accordingly upward, while the Earth's rotation gives 
the Sun the much quicker apparent downward movement 
which carries it below the horizon. Now let us suppose a 
star rising opposite the Sun just as the Sun is setting. The 
star's upward movement due to the Earth's rotation is just 
as quick as the Sun's downward movement due to the Earth's 
rotation ; while the star, unlike the Sun, has no noticeable 
apparent movement due to the Earth's progress in its orbit. 
Consequently, the star must be rising a little quicker than the 
Sun is setting. 

289. About midnight, the Sun will be near the nadir of 
the place of observation. The Earth's motion in its orbit 
will now be eastward, giving the Sun an apparent westward 
motion, which will slightly check its apparent eastward mc 
ment due to the Earth's rotation. The star will be high in 
the sky, and its apparent westward motion will not be checked 
by any apparent movement eastwards. It will continue, then, 
to gain on the Sun. 

290. About sunrise, the place of observation will be on 
the forward side of the Earth as it moves along its orbit. 
The rising of the Sun will be slightly checked by this m< 
ment, while the setting of the star opposite will not thus be 
checked. Accordingly, it" the star rose just as the Sun 
setting (leaving the effect of refraction out of account), it 
must set a little before the Sun rises. 

291. In the course of time, then, as the star is constantly 
gaining on the Sun, it will overtake and pass it. At the end 
of a year from the day when it was opposite to the Sun it will 
again be opposite to it, having apparently, during this time, 
gone round the place of observation once oftener than the 
Sun has gone round it. That is, there would be one more 
day in the year than there is, if we counted days by the rising 
or setting of the stars instead of by the rising or setting of 
the Sun. It appears from this that the period (119) of the 
Earth's rotation is less than what we ordinarily call a day. 



Sec. 291.] Phenomena. 163 

Each day is prolonged for about four minutes by the effect of 
the Earth's movement in its orbit. 

M8« Another result of the fact that the stars are con- 
tinuallv gaining on the Sun is that the stars which we see in 
the evening are not the same from day to day. At any par- 
ticular hour of the evening the stars are a little farther ad- 
vanced in their daily courses than they were at the same hour 
the evening before. Those which were then just setting are 
now below the western horizon ; and some are just rising 
which were then below the eastern horizon. As the seasons 
change, therefore, the appearance of the evening sky likewise 
changes (82). 

MS« The apparent movements of any celestial object which 
are due to the changes of the plane of the ecliptic, or to the 
Earth's movements to one side of that plane or the other, 
are too small to be perceived except by close observation. 
We may therefore suppose for the present that the centres 
of the Earth and Sun are always in the plane of the ecliptic. 
But the Sun is not always an equatorial star, as we have been 
supposing it to be. Only one at a time of the Earth's equa- 
torial diameters lies in the plane of the ecliptic (166); and it 
is only when the equatorial diameter lying in the plane of 
the ecliptic happens also to point to the Sun that the Sun 
;n equatorial star. We have just seen that the motion of 
the Earth round the Sun gives the Sun only a slow apparent 
movement, which will not change its place much in the course 
of a day. Let us suppose, then, that the Sun on some particu- 
lar day is in a line with that one of the Earth's equatorial 
diameters which lies in the plane of the ecliptic. In the 
course of the day the Earth's rotation will have twice brought 
the plane of the ecliptic, one after another, all the equa- 
1 diameti may suppose it to have : and if we 

dkl its motion in its orbit, we may say that 

il diameters has thus been twice pointed 
. .^o that the Sun h nee in the zenith 

and once in the nadir of every part of the equator. During 
a, and in fact for some ore and after, the 



164 Outlines of Astronomy. [Sec. 293. 

Sun seems to move in the sky about as it would seem to move 
if the whole equator of the Earth lay in the plane of the eclip- 
tic. If the Earth, like Saturn, had a ring round its equatorial 
portions, "the edge of the ring would at this time be turned 
towards the Sun (212). 

294. But as soon as the Earth has moved far enough in 
its orbit to make a noticeable change in the position of its 
equator with respect to the Sun, that one of its diameters 
which points to the Sun is no longer an equatorial diameter ; 
and supposing the Earth to have a ring like that of Saturn, 
the Sun has now begun to shine on the northern or the south- 
ern side of the ring. This may be illustrated by the same 
experiment by which the various appearances of Saturn's 
ring, as seen from the Sun, were explained above (213); for 
the inclination of Saturn's ring to the plane of Saturn's orbit 
does not differ much from the inclination of the Earth's 
equator to the plane of the ecliptic. If that diameter of the 
Earth which points to the Sun is not an equatorial diann 
one of its ends must be in the northern and the other in the 
southern hemisphere. Let us suppose that the northern end 
of this diameter is the end nearest the Sun. Then the pl.i 
which have the Sun in their zeniths in the course of a day 
are all north of the equator ; and the Sun passes north of the 
zenith of every place on the equator when it is noon at that 
place. The north pole is in some part of that side of the 
Earth which is turned towards the Sun : so that the Sun is 
all day farther than before above the horizon of the north 
pole, and all day below the horizon of the south pole. Every 
day, as the Earth advances in its orbit, the places which have 
the Sun in the zenith, one after another, lie farther north than 
before ; while the region round the north pole on which the 
Sun never sets, and the region round the south pole on which 
it never rises, are growing larger and larger. 

tiO»>. When the Earth has travelled over about a quarter 
of its orbit since the time when the Sun was passing through 
the zenith of a place on its equator, that equatorial diameter 
of the Earth which lies at the moment in the plane of the 



Sec. 295.] Phenomena. 165 

ecliptic has its ends equally far from the Sun. If we sup- 

c the Earth to have a ring like that of Saturn, the edge 
that ring must at this time he turned as much away from 
the Sun as it ever can be j for it is no more turned towards 
the Sun at one of the places where it crosses the plane of the 
ecliptic than at the other. Any farther advance of the Earth 
in its orbit will bring the edge of the ring more into the sun- 

t at one of these places, and turn it more away from the 
Sun at the other, so that the ring will be placed more nearly 
edgewise towards the Sun. At this time, then, the places 
which have the Sun in their zeniths in the course of a day 
lie as far north of the equator as any places through the 
zeniths of which it passes during the year. They may be 
COOS IS forming the northern boundary of the torrid 

zone, known as the Tropic of Cancer ; although, strictly 

.king, the Tropic of Cancer is a boundary line drawn 
round the Earth, so that one part of it may be as far from the 
equator as another, and so that it may pass in any particular 

r through the most northerly of those places through the 
zeniths of which the Sun passes in the course of that year 
(167). But for a few days at a time, once a year, none of the 
places which have the Sun in their zeniths will be much to 
the south of the Tropic of Cancer. At this time, too, the 

on about the north pole where the Sun continues all day 
above the horizon will take in the whole north frigid zone, 
extending as far as the Arctic Circle. 

IM After this, the places which, one after another, have 
the Sun in their zeniths will be nearer and nearer to the 
equator: while the region of perpetual day round the north 
pole and the f perpetual night round the south pole 

•. tinu illy smaller. When the Earth has come into a 
line with the place from which we supposed it to set out and 
with the Sun. on- bona] diameters again points to 

the Su; >. the places which, one after another, 

have the Sun in their ceoi ^outh of the equator, until 

i • ' • i« orn is that beneath the 

Sun. At this time, the Sun is all day long above the horizon 



166 Outlines of Astronomy. [Sec. 296. 

of any place in the south frigid zone, and does not rise at all 
in the north frigid zone, except near its borders by reason of 
refraction. Continuing its course around the Sun, the Earth 
comes to the place in its orbit from which we supposed it to 
set out, when a year has gone by since the time of its 
passage through that place. 

297. If the apparent direct movement of the Sun oc- 
casioned by the Earth's motion in its orbit were exactly 
contrary to the retrograde daily motion of all celestial obj< 

we could easily tell what appearances would result from both 
movements taken together. Butas they are not exactly 1 
trary, we will resolve the Sun's direct movement into two ; 
one of them exactly contrary to its retrograde movement, and 
the other carrying it due north for about halt* a year at a time, 
and due south for the rest of the year (the words north and 
south having still the meaning in which they are usually ap- 
plied to the Earth). When this northward or soiuhv. 
movement carries the Sun through the zenith of any pi 
on the equator, it is said to cross the equator from south to 
north, or from north to south, as the case may be : and the 
times of year at which it crosses the equator are often called 
the equinoxes. The name equinox comes from the Latin 
words for equal and for night, and is accordingly applied to 
the time when the Sun's daily course is like that of an equa- 
torial star, so as to lie about half above ami half below the 
horizon of all terrestrial places not very close to the poles. 
The times when the Sun stops moving north and begins to 
move south, or stops moving south and begins to move 
north, are often called the solstices; the name of solstice 
being derived from the Latin words for sun and for stand, or 
stop. 

298. When the Sun is a northern star, more than half its 
daily course is above the horizon of any place in the northern 
hemisphere, and more than half of it is below the horizon of 
any place in the southern hemisphere (285). Hence, while 
the Sun is a northern star, it will rise earlier and set later on 
places in the northern hemisphere, and will rise later and 



Sec. 29S.] Phenomena. 167 

set earlier on places in the southern hemisphere, than it does 
while it is a southern star. This will tend to make the 
northern hemisphere warmer than the southern while the Sun 
northern star, and cooler than the southern while the Sun 
is a southern star. But the difference in the lengths of time 
during which the Sun is above the horizon in different days 
is not the chief reason why one day is warmer than another; 
or else the northern parts of Greenland, where the Sun never 
sets all summer long, ought to be warmer at that time of year 
than places near the equator, where the Sun is never above 
the horizon for much more than half of its daily course (28J). 
In fact, however, Greenland is a cold country all the year, 
although not so cold in summer as in winter ; for although 
the Sun shines there long at a time, it never is high in the 
The Tropic of Cancer is not much more than one- 
fourth of the way from the equator to the north pole. Now 
when the Sun is crossing the equator it is near the horizon 
of the north pole : and when it is over the Tropic of Cancer 
it cannot therefore be much more than one-fourth of the way 
from the horizon to the zenith of the north pole or of places 
near it ; while, as seen from any part of the equator, the Sun 
must come once a day to some place in the sky not much 
farther from the zenith than one-fourth of the way from the 
zenith to the horizon. 

Mli There are two reasons why the height of the Sun in 
the sky should make a difference in the warmth we get from it. 
In the first place, much more of the Sun's warmth is cut off 
from us by the air when the Sun is low than when it is high ; 
beat, like light, is absorbed by any atmosphere through 
which it passes (74, 192). Accordingly, when the Sun is 
near our horizon, part of the heat sent out from it towards 

r over pi 1 es between us and 

that the Sun in its zenith. But secondly, 

• no air, the ground around us would be lesa 

the Sun than as mu<h ground in a place from 

wn > i higher in the sky. If a fence stands 

md, the nun, Us which we should 



168 Outlines of Astronomy. [Sec. 299. 

pass in a hundred steps taken alongside of the fence would 
be greater than the number we should pass in a hundred steps 
of the same length alongside of a fence standing on sloping 
ground and having upright posts as far from each other as 
those of the first fence. So, too, if a shower of rain falls t 
tically on a hill at the top of which there is a piece of level 
ground, more raindrops must fall on a square yard of the level 
top of the hill than on a square yard of the sloping ground on 
its sides. Again, if any flat object stands nearh ie to 

the point of sight in a projection of any kind, it will be repre- 
sented in the projection as a much smaller object than another 
which is really no larger, but which nearly faces the point of 
sight (270). All these examples show that a level piece of 
ground facing the Sun, or, in other words, having the Sun in 
its zenith, will get more heat from it than a level piece of 
ground of the same si/.e standing nearly edgewise to the Sun, 
or, in other words, having the Sun near its horizon. If a 
projection of the Earth should be made, with the point of 
sight taken anywhere on the Sun. the shapes of the count 
which had the Sun high in their sky at the time of the projec- 
tion would be pretty correctly shown, while the places which 
had the Sun low in the sky would be much crowded together 
round the edge of the projection. 

30<K The course of the seasons, then, depends chiefly on 
the height in the sky which the Sun daily reaches at different 
times of year. In the torrid zone all times of year are hot, 
because the Sun passes every day not far from the zenith. In 
the middle parts of the temperate zones the summer is hot, 
because then the Sun daily passes near the zenith, and the 
winter is cold because the Sun then never rises far above the 
horizon. In the frigid zones the weather can seldom be called 
hot, because the Sun is never high in the sky. although it is 
so long above the horizon in summer that the weather then 
is much less cold than in winter. The hottest weather of 
summer usually comes somewhat later than the day on which 
the Sun passes nearest to the zenith ; for the ground and air 
require time to become heated, and also require time for 



Sec. 300.] Phenomena. 169 

becoming cool again. In like manner,*the greatest heat of 
any particular day comes some hours after noon. 

SOI. Until recent times, all highly civilized nations of 
i story any record has been preserved have lived in 

north temperate zone or in the northern parts of the torrid 
zone. Accordingly, the names which are usually given to the 
equinoxes and solstices are suited to the seasons of the north 
temperate zone. The equinox at which the Sun crosses the 

ttor from south to north is called the vernal (or spring) 
equinox ; the solstice at the time of which the Sun is in the 
zenith of some place on the Tropic of Cancer is called the 
summer s the following equinox is called the autum- 

nal equinox, and the next solstice is called the winter sol- 

:>0\>. If the time when the year should be considered to 
gin were now to be settled for the first time, it is likely 
that the vernal equinox would be chosen for this purpose. 
But it is always inconvenient to make changes in any ar- 
gument which has once come into use ; and when the first 
satisfactory plan for keeping particular months to particular 
sons was contrived, it was thought best to begin the first 
r in which the plan was tried at the time of the first new 
moon after a winter solstice, although the plan itself had 
nothing to do with the Moon. Accordingly, the winter 
itice still comes a little before the end of every year, 
although we do not reckon the beginning of the year by any 
new moon. Hence the summer solstice comes towards the 
end of June, and the equinoxes towards the ends of March 
and September. 

:;<K. e Earth's orbit is so situated at present that the 

i perihelion about the beginning of the year, 

and its apheli in July. It is therefore nearer the Sun 

aiter than in the summer of the northern hemisphere. 

But orbit is too small (146) to 

allow this 1 ince to make much di (Terence in the 

.: times of year or in dif- 
irtfa ; although a sunny day in December 



170 Outlines of Astronomy. [Sec. 303. 

in the southern hemisphere is no doubt likely to be still hotter 
than a sunny day in June in the northern hemisphere. 

30-1. Since the Earth moves quicker in its orbit the nearer 
it is to the Sun (148), the time from any vernal equinox to the 
next autumnal equinox after it must be a little more than half 
a year. The exact times of the equinoxes and solstices in 
any particular year may be found in carefully calculated 
almanacs. For common purposes it is correct enough to 
say, as people usually do, that the vernal equinox comes on 
March 21, the summer solstice on June 21, the autumnal 
equinox on September 21, and the winter solstice on Decem- 
ber 21. As February, which is the shortest month, comes 
just before March, this will agree With the fact just stated, 
that the time during which the Sun is a northern star 
little longer than that during which it is a southern star. But 
the time from the vernal to the autumnal equinox is still 
longer than the time from March 21 to September 2 1 . ->«» that 
we shall be more accurate if we put the solstices and the 
autumnal equinox a day or two Liter than the 21st of the 
months in which they come. Although the Earth DOW pas 
its perihelion about January I, this will not always be the 
case, since the slow change of the Earth's orbit already 
mentioned (169) makes the time when the Earth passes its 
perihelion a little later every year than it was the year be: 
But this change is so slow that it would alter the time of the 
Earth's perihelion passage less than four days in a thousand 
years. The Earth's precessional movement (167) does more 
than the change in its orbit to increase the time from the 
winter solstice to the perihelion passage. The Earth's equator 
is turned edgewise towards the Sun, by the retrograde pre( 
sional movement, more frequently than would otherwise be 
the case. That is, the year is shortened a little by the 
EartVTs precessional movement. Hence the Earth's peri- 
helion passage would be later in the year every time it 
happened than it was the time before, even if the Earth's 
orbit did not change. But the change in this orbit and the 
precessional movement, taken together, would alter the time 



Sec. 304.] Phenomena. 171 

of the Earth's perihelion passage less than twenty days in a 
thousand years ; and the differences between the times of the 
equinoxes, solstices, and perihelion passages of successive 
years, lis found in the almanacs, are elderly due to the facts 
that the leap years are each one day longer than the others, 
and that the Earth's movement round the Sun is not exactly 
in the ellipse called its orbit, but is subject to certain pertur- 
bations (170). 

SO.>. We have now considered the effects upon the 
sons, and upon the Sun's place in the sky, of its yearly 
movement northwards and southwards. The chief effect 
of its movement exactly contrary to the general retrograde 
movement oi all celestial bodies is that the other stars seem 
10 be always gaining upon it, as described above (291). But 
this lagging of the Sun among the stars is sometimes greater 
than at other times ; and we will now consider why its rate 
chang 

300. When any object is regarded as having two move- 
ments at once, the amount of its whole movement for any 
length of time is commonly less than the separate amounts, 
for the same time, of its two movements added together; and 
supposing its whole movement to carry it over equal dis- 
tances at two different times, while one of its two movements 
^reater at the first time than at the second, it does not 
follow that the other movement must be greater at the second 
time than at the first. Still, in the case we are to consider, 
it happens, as would naturally be supposed, that the greater 
is the northward or southward movement of the Sun while its 
whole movement comes to any particular amount, the less is 
£, movement ; although the decrease of 
one movement will by no means be equal to the increase of 
the of 

B07« of the Sun's movement from north- 

BOUthward, or from southward to northward, is not 

sue' lai That is, for some time before and after 

either of the solstices, the Sun moves little either northward 

uuthward ; while at either of the equinuxes its northward 



j] 2 Outlines of Astronomy. [Sec. 307. 

or southward movement is a larger part of its whole movement 
than at any other time, and becomes less and less in propor- 
tion to its lagging movement as it approaches the next 
stice. It lags most at the solstices, then, and least at the 
equinoxes, in proportion to its whole direct movement at 
those times. 

308. The whole direct movement of the Sun is quicker the 
nearer the Earth is to its perihelion ; for not only does the 
Earth move quicker the nearer it is to the Sun (148), hut 
the greater is the Sun's apparent movement due to the Earth's 
movement round it ; just as the objects nearest to a moi 
railway train seem to its passengers to move quicker than 
others at a greater distance. Since the Sun's whole direct 
movement is thus, in our times (303), quicker while the Sun 
is a southern star than while it is .1 northern star, both its 
northward and southward, and also its lagging, movements are 
on the whole greater from the autumnal to the vernal equinox 
than for the rest of the year. 

305). It follows, then, that the stars gain on the Sun more 
at the winter solstice than at any other time of year. They 
gain on it rather more than usual about the time of the sum- 
mer solstice, although much less than at the winter s 
and about the equinoxes they gain on it less than usual. If we 
compare the Sun's daily movement to the movement of the 
hand of a clock, we may say th.it it is fast losing at the time 
of the winter solstice, losing less at the time of the summer 
solstice, and losing still more slowly at the time of the equi- 
noxes. 

310. For all ordinary purposes, we must make our clocks 
keep time pretty nearly with the Sun ; but it would be incon- 
venient, as well as difficult, to make clocks change their r 
with the Sun. They are therefore so made that the number 
of days in a year counted by means of a clock is the same 
with the number of clays in a year according to the Sun, 
although the length of every day is the same according 
to the clock, while according to the Sun different days 
have different lengths. Suppose that we have so good a 



Sec. 310.] Phenomena. 173 

clock that it will run for a year at a time without either 
gaining or losing. We can set it so that on any day in the 
year when we please both its hands will point to twelve at the 
time when the Sun is highest in the sky. We may set it, if 
we prefer to do so, so that its hour hand points to six and its 
minute hand to twelve when the Sun is in the plane of the 
rational horizon (264) ; or so that it will agree with the Sun, 
as in the instances just given, at any time of any day in the 
year. The time actually chosen for this purpose is a little 
after the winter solstice ; the reason of this choice depends 
on the terms used in practical astronomy, and need not be 
considered here. A little after the winter solstice, then, a 
sundial will agree with a good clock. But at this time the 
stars are gaining rapidly on the Sun ; and considering the 
Sun as the hand of a clock, it is running unusually slow. 
Hence the sundial will lose time for several weeks, until it is 
about fifteen minutes slow of the clock. Then it will begin to 
gain on the clock, and will overtake it a little after the vernal 
equinox. It will go on gaining until the summer solstice ap- 
proaches, when it will begin to lose ; but its gain and loss at 
this time of year are comparatively small, so that it keeps 
within five or six minutes of the clock. Shortly before the 
summer solstice it will have fallen back so much as to agree 
with the clock again, after which it goes on losing for a time, 
and then gains rapidly, passing the clock and getting over 
fifteen minutes in advance of it before it begins to lose again. 
A year from the time chosen for the first agreement of the 
clock and sundial, they will of course agree, if the clock has 
kept good time. 

311. A dock so regulated as to go on running in the man- 
ner just described, is said to keep mean time. If it is com- 
pared with the Stars, it must be considered as losing one day 
in the y Ise the stars must be considered as gaining 

one day in the year. But by shortening the pendulum of the 
tsily make it go fast enough to keep up with 
the r to speak more exactly, with any particular star 

we plea.se ; lor, as we have seen, the stars as seen from the 



174 Outlines of Astronomy. [Sec. 311. 

Earth change their places slightly with respect to each other, 
by reason of their own real movements as well as by reason 
of real movements of the Earth, some of which belong to the 
whole Solar System, and not to the Earth alone. If we place 
a thin flat metal plate exactly north and south, and exactly 
vertical, fastening it so that it cannot change place with re- 
spect to the Earth, we may regard the Earth as the wheel 
of a clock and the plate as the hand carried by that wheel. 
Any star the daily course of which is a sufficiently large ring 
will answer to a mark to which the hand points upon the dial 
of the clock. We may now take a number of clocks of the 
usual kind, and try to regulate them so that one day accord- 
ing to these clocks shall be just equal to the time between 
the moments when the star comes opposite to the edge of the 
plate on one evening and on the next. We shall find that the 
intervals of time at which the Earth's rotation brings the plate 
back to the star are more nearly equal to each other than are 
the days marked by the best clocks that can be made. The 
Earth turns more uniformly than the wheels of our clocks, 
and those movements of the star which are not uniform are 
so small or so slow that they will interfere much less with 
the regular return of the plate to the star than the defects of 
our clocks interfere with their regular running. Still, since 
it is a known fact that stars have movements which are not 
uniform, it would not be convenient to regulate clocks by the 
movements of any particular star. When it is desirable that 
a clock should on the whole keep time with the stars, the 
effect of the Earth's precessional motion, as well as of its 
rotation, is taken into account ; and the clock is so regulated 
that it may run as nearly as possible at a certain rate found 
by calculation. The time which would be shown by a clock 
which always went exactly at this rate, and had been started 
exactly at the moment required by calculation, is called side- 
real time. There are some stars according to which, on 
account of the Earth's precessional motion, the day would be 
a little shorter than it is by sidereal time ; but according to 
most of the stars, the day would be a little longer than it is 



Sec. 311.] Phenomena. 175 

by sidereal time. However, as most of the stars lose little 
over three seconds a year on sidereal time, the error of a side- 
real clock can easily be determined by observations of stars 
and a few simple calculations. It is easier to find the exact 
sidereal time in this way and then to calculate the exact mean 
time for the same moment than it is to get the mean time from 
the Sun. observations of which are not likely to be as accurate 
as observations of the stars. But at sea, the time is usually 
found by means of the Sun. Most of our clocks and watches, 
however, are regulated by means of comparisons made be- 
tween some of them and the clocks regulated to sidereal time 
which are kept at astronomical observatories. A sidereal 
clock is of little use for the common purposes of life, because 

gains one day in every year on an ordinary clock, and 
therefore never agrees with it except at the time of the 

Dal equinox, which is the time that has been chosen for 
this agreement, although any other time of year might of 
course have been chosen for it. About the time of the 
autumnal equinox, therefore, the day is half over by a side- 
real clock when it is just beginning by a mean time clock. 

31^. Two clocks of the same kind, one of which is just 
north of the other, will always agree if they are running cor- 
rectly, no matter how far apart they are upon the Earth. But 
if either is at all east of the other, the time shown by the east- 
ern clock should be later than that of the other in proportion 
to their difference of longitude, as that word is used in geog- 
n. is a mere matter of convenience. Clocks 
night be snow the same time in all parts of the 

h at any particular moment, and in some respects this 
arrangement would be more convenient than that now in use. 
But we are us tving the day begin at the time of mid- 

k ; and this time is nearly, 
allh in the middle of the night (310). 

The middle of the night at any place must be the time when 
tne : turned that place so tar away from 

the Sun that a line from it pointing to the Sun's 1 entre will 
cross the line of the Earth's axis. This cannot happen at 



176 Outlines of Astronomy. [Sec. 312. 

once in any two places, one of which is not due north of the 
other; so that if people agreed to begin the day at the same 
time all over the Earth, they could not all begin it about the 
time of midnight, which would be puzzling until they had 
grown used to the new arrangement The mean time, 
sidereal time, used at any particular place is called local 
mean time, or local sidereal time. 

313. The local times of the ends of any diameter of the 
Earth must be twelve hours, or half a day, apart ; unless this 
diameter is the axis, or polar diameter, at the ends of which 
there is, strictly speaking, DO local time, tor want of" any 
mark of noon or midnight All places north and south of 
the end of any diameter have the same local time with that 
end. Accordingly, the local times <>t two places, the short- 
est route between which, upon the Earth, leads directly I 
one of the poles, must differ by half a day. If two men 
travel from any place, one eastwards, and the other w 
wards, to some place the local time of which differs | 
day from that of the first place, then the day of the week or 

month, according to the traveller who went eastwards, will 
be the day after that which is the day of the week or month 
according to the other traveller's reckoning. For the travel- 
ler who went eastward has been through a 
the local time of each of which is a little Liter at any particu- 
lar moment than the local time of the place next to it on the 
west. The difference of half a day between the pi. ices at the 
beginning and end of his journey will accordingly make his 
reckoning half a day later than the local time of the pi 
from which he started, while for a like reason the other trav- 
eller's reckoning will be half a day earlier; so that the I 
reckonings will differ by a whole clay. America was settled 
by Europeans who came to it westwards, while the Euro- 
pean settlements in the East Indies were made by color, 
who travelled eastwards. Consequently, wh< n any traveller 
crosses the Pacific Ocean, he finds, if he comes from the 
East Indies to America, that the day which is Wednesday, 
for example, according to his reckoning, is called Tuesday in 



Sec. 313.] Phenomena. 177 

the place at which be lands ; and if be comes from America to 
the East Indies, he rinds that what is November 3, for exam- 
ple, by his reckoning, is called November 4 on shore. The 
name of any particular day at European settlements on 
islands in the Pacific Ocean depends on the places from 
which those islands were settled. This is one of the incon- 
veniences of using local time, but it makes little trouble 
ept that of learning the reason of it. 

311. If a traveller should reach one of the poles of the 
Earth, and could determine its place with great precision, he 
could of course change his local time half a day by walking 
half round the pole, or a whole day by walking entirely round 
it. So too, if we ourselves could travel as fast as we can 
send a telegraphic message, we could change almost at once 
from one local time to another very different local time. If 
we had this power, we should find it easy to understand that 
our reckoning of local time is merely a convenient arrange- 
ment which might be changed without altering any astronom- 
ical iphical facts. 

SU« Even at any one place different people may adopt 
different plans of reckoning local time. Sailors and astron- 
omers, for instance, prefer to begin the day at noon rather 
than at midnight. Astronomers begin their days twelve 
hours later than most other people, so that the second of 
March, for instance, in astronomical mean time, is made up 
of the last half of the second and the first half of the third of 
rch in ordinary civil time. According to Bowditch's Nav- 
>r. the nautical day begins twelve hours sooner than the 
civil day : at present, however, sailors often follow the astro- 
nomical rule. 

31fi. What is commonly meant by the time of day, among 

the civilized nati< :ropean descent, is the local mean 

civil time of some important place in the same country with 

that where this time is spoken of. It would be troublesome 

to i g from one local time to another when- 

•' we went from one house to another, or even from one 

another. Hence the local time of a large city, or 

12 



178 Outlines of Astronomy. [Sec. 316. 

more accurately, of some particular place in a large citj 
pften used for many miles around the city. Thus, in the 
United States, we often hear of Washington time, New York 
time, and so on ; especially when we travel long distances 
eastward or westward. 

317. Astronomical clocks are generally made with dials 
showing twenty-four hours, so that the hour hand goes round 
its dial only once a day instead of twice, as in ordinary 
clocks. The hours of the day have sometimes been counted 
in this manner by other people than astronomers ; and 
sunset has often been chosen for the beginning of the day 
instead of midnight or noon, but only in places where time 
was roughly reckoned by the sunset actually observed instead 
of by good clocks. The time shown by a sundial is called 
either true or apparent time ; names which seem hardly 
applicable to the same thing. Now mean noon, as we have 
seen, never differs much more than a quarter of an hour from 
true or apparent noon (310) ; while the time of sunset, except 
at places near the equator, varies considerably at different 
times of the year. 

318. The reason why the local times of sunset and sun- 
rise change more than the local time of true noon with the 
time of year is of course the lengthening and shortening of 
the nights resulting from the Sun's northward or southward 
movement. This movement lengthens or shortens the night 
as much at one end as at the other ; so that while it changes 
the times of sunrise and sunset, it leaves the times half-way 
between sunrise and sunset unchanged. These times must 
of course be very near the times of true noon and true mid- 
night. Meanwhile, since the Sun's direct movement is not 
uniform, the remaining part of it somewhat changes the local 
time of sunrise and sunset as well as of noon and midnight. 
The course of these changes for any particular part of the 
Earth may be easily followed. 

319. Suppose, for instance, that we are at any place in 
the north temperate zone of the Earth, and that the winter 
solstice is just passed. True noon now comes at twelve 



Sec. 319.] Phenomena, 179 

o'clock (310), while sunrise comes considerably after six 
I <ck in the morning and sunset considerably before 
o'clock in the evening ; for the Sun is so far south that 
we see much less than half of its daily course (298). At this 
time the Sun's northward movement is slow (307), and it is 
losing fast as compared with the clock (309). This lagging 
of the Sun makes the sunrise, noon, and sunset of each day 
somewhat later than those of the day before it; while the 
rthward movement of the Sun does little more, in 
making each sunrise earlier than the last, than is enough to 
balance the contrary effect just stated. But all that it does 
in making each sunset later than the last goes to increase 
the effect of the Sun's lagging behind the clock. Accord- 
ingly, the time of sunrise differs little from day to day for 
end weeks after the winter solstice, while the time of sun- 
er rather quickly. 
:>\M>. As the vernal equinox approaches, the northward 
movement of the Sun becomes quicker, and begins to have 
much effect in making sunrise earlier and sunset later. Mean- 
while, the Sun has begun to gain on the clock, which makes 
sunrise a little earlier still than it would otherwise be, and 
also makes sunset a little earlier, which tends slightly to 
check the effect of the Sun's northward movement in making 
sunset later: so that in early spring sunrise grows earlier 
more quickly than sunset grows later. 

o'M. During the summer, the contrary effects of the 
rth's place in its orbit and of the occurrence of the sci- 
fi (3°7» 3°8) keep the Sun in pretty good agreement with 
the clock (310), so that the times of sunrise and sunset 
depend mainly on the northward and southward movements 
of the Sun. In early autumn, however, while the Sun is fast 
I on the clock, sunset must grow earlier more quickly 
than su- : and when the winter solstice is 

dial the Sun is in advance of the clock, but is quickly 
llthward movement of the Sun 
. the time of sunrise grows later more quickly than 
rfailc that of sunset has alrt :\ nearly as early 



180 Outlines of Astronomy. [Sec. 321. 

as it is to be, and continues with little change for some time. 
The effect of the Sun's various movements on the times of 
sunrise and sunset at any particular place may be followed 
out by the help of the explanations already given. The 
northward and southward movements of the Sun can have 
no effect of this kind at places on the equator, where half its 
daily course is in sight whether it is a northern or a southern 
star (285). On the other hand, when the Sun has once risen 
at either of the poles, it will not set again till about the time 
of the next equinox, but will go spirally round the sky until 
it has risen at the solstice about one-fourth of the way to 
the zenith (298), after which its course round the sky will 
gradually fall back again towards the horizon, and at length 
below it. 

8&S, The best way to get clear notions of the daily and 
yearly changes above described, is to watch the stars until 
their daily courses have become familiar, and until the equa- 
torial and circumpolar stars (284) can easily be distinguished 
at all times of year, even if the names of the separate 
stars of each kind are not known. Sufficient observation of 
this sort will enable any one to learn the apparent yearly 
course of the Sun among the stars (292) ; for although the 
stars among which the Sun would appear to be at any partic- 
ular time, if they could be seen, are in fact invisible ov 
to the Sun's brightness, yet we can watch the stars which 
seem just before sunrise and just after sunset to be nearest 
to the Sun. In this way we notice that the Sun is always 
moving towards some of the stars seen after sunset and away 
from some of the stars seen before sunrise, so that a star 
which sets on any evening soon after the Sun, and at nearly 
the same place with it in the horizon, can no longer be seen 
a few evenings later, and after some time rises just before 
sunrise nearly where the Sun appears on the same morning 
shortly afterwards. The stars near which the Sun seems to 
pass are equatorial, northern, or southern stars (286), accord- 
ing to the time of year at which they are passed. The Sun's 
course among them is so nearly the same from year to year, 



Sec. 322.] Phenomena. 1S1 

no change can be noticed in it without very careful 

lions. This course is the imaginary line called the 

ecliptic. It is in fact a projection of the Earth's orbit on 

" )• 
:»\*'». The zodiac is the name given to a belt or strip of 
boundaries, but considered as includ- 
es near the ecliptic on both sides (277). If we 
are acquainted with these stars, we can see on any evening 
through what part of the sky the zodiac then extends. The 
equatorial stars may be regarded as forming another belt, 
whi a from any one place, always extends over the 

irt of the sky, forming an arch which meets the east- 
ern and western-parts of the horizon (-^-)< and passes north 
the zenith, according to the situation of the ob- 
'Uth or north of the equator. The stars which form 
differ with the seasons (292), but the place of the 
- the same. The zodiac must cross this equato- 
rial belt of stars at the two opposite places where the Sun 
ma to be when it is an equatorial star ; or, in other words, 
re the Sun seems to be at the time of the equinoxes. 
Tin l themselves are often called equinoxes, and the 

parts of the zodiac which are farthest north and south of the 
equatorial belt of stars are often called solstices, because at 
the • es the Sun seems to be in those parts 

. A more precise meaning than this is given 
in i - will be seen, to the terms equinox 

and solstice when they are us enote places; but the 

: our present purposes. 

:; "- 1 - r the appearance of the zodiac 

the time of the vernal equinox. The 

DOW just below the western part of 

the horizon, and the p] the autumnal equinox just above 

a. The part of the zodiac in 
tO tiav( rse during the next 
re form an arch from east to \ 
equatorial si 
Earth half a the equator 



182 Outlines of Astronomy. [Sec. 324. 

to the Tropic of Cancer, the zodiac must now pass about as 
far north of the zenith as the highest equatorial stars are 
south of the zenith. To an observer still farther north, the 
arch formed by the zodiac must seem more nearly upright 
than the arch formed by the equatorial stars. 

32*3. Just after sunset at the time of the summer solstice 
the autumnal equinox will lie among some of the highest 
equatorial stars, so that the zodiac will cross the sky from a 
place north of the western to one south of the eastern part 
of the horizon. Just after sunset at the time of the autumnal 
equinox the zodiac will cross the sky from east to west again, 
but will pass south of the highest equatorial stars, so that to 
an observer in the north temperate zone, for instance, it will 
form an arch leaning far towards the southern horizon. Just 
after sunset, at the time of the winter solstice, it will reach 
from north of east to south of west. 

326. The planes of the orbits of the Moon, and of all the 
planets which are easily visible, differ so little from the plane 
of the ecliptic that the objects moving in them must always 
appear to be somewhere in the zodiac. This fact will help 
us to understand the appearances occasioned by the mo 
ments of the Moon and planets, now that the effect of the 
Sun's movements has been considered. 

327. Two celestial objects are said to be in conjunction 
with each other when they appear to be near each other in 
the zodiac ; and to be in opposition to each other when their 
places in the zodiac are nearly opposite to each other, so that 
one of them is half-way from its rising to its setting when 
the other is half-way from its setting to its rising. One 
object is in quadrature with another when half-way between 
conjunction and opposition with it. All these terms are used 
with a more exact meaning in practical astronomy than ap- 
pears from this explanation, which is sufficient, however, for 
our present use. When any object is said simply to be in 
conjunction or opposition, the Sun is understood to be the 
object with which the conjunction or opposition is made. 

328. An inferior planet (198) cannot be in opposition to 



32S.] Phenomena. 183 

the Sun, but may come into conjunction with it in two ways : 
it may pass nearly or exactly between the Sun and Earth, 
or it may pass nearly or exactly behind the Sun as seen from 
the Earth. In the first case the conjunction is inferior, in 
the second case superior conjunction. When it passes 
reen the Sun and the Earth it must appear as a 
black spot crossing the Sun's disk. This appearance is called 
a transit oi the planet. 

:5\M>. A superior planet (199) can have no inferior conjunc- 

I the Moon can have no superior conjunction; but 

q may be in opposition to the Sun, and so may any 

superior planet. When the Moon passes exactly between 

.: 1 of the Earth and some part of the Sun, the Sun is 

eclipsed. 

SSO. JUed up by the Sun, and either in 

opposition to it, or in superior conjunction with it, will have 
wards the Earth ; if in or near inferior con- 
junction with the Sun, its side seen from the Earth will be 
wholly or nearly dark. In tins way arise the appearances 
which are called phases of the Moon and planets. The 
I to be new either when it is in conjunction with 
the Sun, or as soon afterwards as it can be seen. It then 
app< l it crescent east of the Sun, not giving light 

to be seen until after sunset. A flat disk would be 
(I up all over as soon as it was turned at all 
the Sun ; so that the appearance of the new moon 
sh<- the Moon Jar, bulging out towards us so 

bo cut off the sunlight from the parts of its disk at a dis- 
tance from the preceding limb, which is that now turned 
At this time the terminator (194) is 
shaped like half an ellipse, because it is a projection (270) 
of the boui. 'een the light and dark parts of the 

Moon, and this l>oun< over ground which bulges out 

tow .ir its quadrature with the 

Sun, the terminator is ne.i the boundary 

of which it I then seen nearly edgewise. 

; the elliptical and straight 



184 Outlines of Astronomy. [Sec. 330. 

lines, representing circles, which are usually drawn upon maps 
of the Earth. 

331. Any globular body has a gibbous appearance when 
seen in such a light that more than half but not the whole of 
its disk is illuminated. The Moon is accordingly gibbous 
between its quadratures and its opposition. When near oppo- 
sition, it is said to be full. The faint illumination of the Moon 
by the Earth has been noticed above (193). 

332. Venus and Mercury, on the other hand, are full only 
about the times of their superior conjunctions, when they are 
too nearly in a line with the Sun to be seen. Their phas 
or the changes of shape in the illuminated parts of them 
which can be seen from the Earth, cannot be noticed with- 
out telescopes, mainly by reason of irradiation (193.) Some 
people, however, think they can see at times that Venus 
not quite round. When the boundary between the light and 
dark parts of an inferior planet is turned edgewise to the 
Earth, it appears as a Straight terminator, and the planet's 
disk, as seen through a telescope, looks like a half moon. 
About this time the planet seems to be as far away from the 
Sun in the zodiac as it is to go between its last and next 
conjunctions. This does not happen half-way between one 
conjunction and the other, for the same reason for which a 
ring put edgewise into a funnel touches the sides of the fun- 
nel at two places which are nearer together than the full width 
of the ring. If the ring is supposed to be viewed from the 
bottom of the tapering part of the funnel, it must seem wi< 
where it touches the funnel instead of where it is reallv 
widest (267). In like manner, the orbit of Venus, for in- 
stance, looks widest to a terrestrial observer where straight 
lines drawn to it from his station would just touch it and pass 
on without crossing it. The places in the planet's orbit 
touched by these lines seem to the observer to be farthest 
from the Sun ; and when the planet is at one of these places 
it is said to be at its greatest elongation east or west of the 
Sun, as the case may be. 

233. Between one of its elongations and its superior con- 



Phenomena. 1S5 

junction a planet like Venus or Mercury must appear gibbous. 
either of its elongations and its interior conjunction 
it must . s a crescent. It will look brightest at some 

time when it i crescent, because its approach to 

the Earth as it comes towards its inferior conjunction will 
more than make up for the turning away from us of its bright 
-. until the crescent which it shows us has become very 
narr 

•rior planets cannot appear as crescents, or 
- half moons, because they have no inferior conjunc- 
: quadratures with the Sun, Mars looks 
is, and Jupiter slightly gibbous. We never 
the line joining Saturn with the Sun to 
make it appear even slightly gibbous ; and of course, there- 
I'ranus and Neptune can show no phases. 
335. The time between one new moon and the next, or 
between one superior conjunction of any planet and the next 
superior conjum: the same planet, cannot be the same 

as the period of revolution of the Moon about the Earth or 
of the planet about the Sun. For all conjunctions and oppo- 
sitions depend on the place of the Earth in its orbit as well 
DO the places of the b< served to be in conjunction 

or opposition. The time from one conjunction to the next 
conjunction of the same kind, or from one opposition to the 
ncx* ed the time of ical revolution of the 

ct under con- i. The time of its sidereal revolu- 

h it occupies in once traversing the whole 
ection of the place around which it 

C ecliptic the projection of the 

The time of the anomalistic revolution 
Of its perihelion pas- 
'-•s and tl ■ r, in the < llite, between two 

of K1 • to that p orbit where it is 

nearest to t h it moves. The sidereal 

- what w • md by the revolution 

il>out another, unless that revolution is expressly 
stated to be synodi malistic. 



186 Outlines of Astronomy. [Sec. 336. 

336. The Moon keeps the same side to the Earth because 
the period of its rotation agrees with that of its sidereal revo- 
lution (177), but in other respects this sidereal revolution of 
the Moon is unimportant to us in comparison with its synod- 
ical revolution, on which depend, as we have just seen, its 
changes of appearance. The time of one of the Moon's 
synodical revolutions is often called a lunation. During 
every lunation the Moon completes one sidereal revolution 
and begins another ; for its real motion and the Sun's appar- 
ent motion among the stars are both direct. Hence, when it 
arrives at the place in the zodiac from which it started, the 
Sun has moved some distance beyond its place at the begin- 
ning of the Moon's sidereal revolution, so that the Moon has 
to go farther before it is again situated in the zodiac as it then 
was with respect to the Sun. One lunation occupies about 
twenty-nine and a half days. 

337. The divisions of time called months were originally 
meant to agree with lunations; but as there are betwi 
twelve and thirteen lunations in a year, and as it was found 
inconvenient to begin the year except at the beginning of 
some month, the months finally came to be mere customary 
divisions of the year, not answering to any astronomical 
events. 

338. The small differences in the apparent movements of 
the Moon due to the changes of the plane of its orbit, and of 
its orbit in that plane, produce no effects which need here be 
considered. We need only inquire how far the appearance 
of the Moon when it is new or full depends on the place of 
the zodiac at those times. Let us suppose that it is new 
moon about the time of the vernal equinox, and that we are 
placed in the north temperate zone. The arch in the evening 
sky now formed by the zodiac is more upright than usual 
(324), so that the Moon is nearly over the place where the 
Sun has just set. In this case the lower limb of the Moon 
will be turned to the Sun, so that the horns of the crescent 
will seem to be more nearly than usual on a level with each 
other. If the time is that of the autumnal instead of the 



$$S.] Phenomena. 187 

vernal equinox, the arch of the zodiac will slant towards the 
. and the Moon will appear to us so much to 
the leu of the Sun that its crescent will be more nearly up- 
it than usual. At other times of year the crescent will 
it more or less towards the horizon according to the place 
of the zodiac in the sky. and to some extent according to the 
place north or south of the ecliptic, in the zodiac; 
but this makes comparatively little difference in its appear- 
The farther we are from the equator, the greater will 
be the di in the appearance of the new moon at differ- 

ent times It is curious that the slant of its crescent 

! the horizon has been taken by some people for a 
or dry weather. Those who made this blunder 
must have been card servers not to notice that like 

appearances returned in order every year. 

SS9. The full moon is seen in the part of the zodiac oppo- 
to the Sun. Accordingly, when the Sun is an equatorial 
: the full moon is also among the equatorial stars ; when 
the Sun is a southern star the full moon is among the north- 
ern 1 id when the Sun is a northern star the full moon 
mong the southern stars. Hence about the time of the 
winter solstice the full moon rises far north of east and sets 
north of west ; and the full moon is longest above the 
horizon at that time of year when the nights are longest. 
340. Although the direct motion of the Moon carries it 
e zodiac much more quickly than the Sun is carried 
lloag the zodiac by its apparent direct motion, the retrograde 
on of the Moon, due to the Earth's rotation, is still 
qui I ' we might count days by the Moon, if we 
cho- jled lunar days, and their 

Lfl the length of a sidereal day 

Itar may be measured (311). 

the Earth so that it 

•her 
due west, the lu: inning or 

ending when the Mo- ve the horizon is opposite 

the edge . . tight regulate a clock to such a 



188 Outlines of Astronomy. [Sec. 340. 

rate that the number of days in a year according to this clock 
would be equal to the number of lunar clays in the same year. 
The clock would have to lose about forty-nine minutes a day 
as compared with an ordinary mean time clock, because the 
Moon lags more than the Sun, so as to lose about a day of 
mean time in any single lunation. But it does not follow that 
the Moon will rise forty-nine minutes later every day than it 
did the clay before. Different lunar days differ in length still 
more than different solar days ; so that the Moon would be 
found to gain and lose on a clock so regulated as on the 
whole to keep time with it much more than the Sun gains and 
loses on mean time clocks. The Moon's speed in its orbit 
varies during each of its revolutions round the Earth ; and 
the changes of its orbit are quick compared with those of the 
Earth's orbit. But even if it kept exact time with a suitably 
regulated clock, the times of its rising and setting would be 
changeable compared with those of the Sun ; for its direct 
movement may be resolved into others, just as the Sun's 
direct movement was resolved above (297). Now, since the 
Moon's whole direct movement along the zodiac is much 
quicker than the Sun's, its northward and southward m< 
ment is sometimes much quicker than the Sun's, while at 
other times, when the Moon is near a solstice (322), it must 
come to a pause ; so that its speed changes more than the 
speed of the Sun's northward and southward movement, and 
this change of speed will make the time of moonrise still more 
changeable than the time of sunrise (31S). The rising of the 
Moon is seldom noticed except at the time of full moon ; for 
at other times it happens either while the Sun is still above 
the horizon or late in the night. We will therefore consider 
only those changes in the time of moonrise which happen at 
full moon and at places in the north temperate zone. 

341. When the Moon is full in spring, it must be near the 
place of the autumnal equinox in the zodiac ; for the Sun is 
then near the vernal equinox (324). Every evening, then, 
the Moon is farther south, and must on this account rise 
later, than the evening before. Accordingly, there is now an 



Sec. 341.] Phenomena. 1S9 

unusually large difference by a mean time clock between one 
arise and the next. In autumn, the Moon is near the 

lal equinox when full, and its northward movement, which 
is at this time unusually quick, greatly lessens the ordinary 
delay of its rising, which is clue to its lagging behind the 
Sun. Hence any full moons which occur from the latter 
part of August to the latter part of October will rise for 

era! evenings in succession much more nearly at the same 
mean time than usual. Full moons of this kind have been 
called harvest moons when they come about the time of har- 

\ and hunter's moons when they come in October. From 
a place far enough north, a harvest moon may be seen to rise 
earlier than it did the night before, instead of later. In places 
about half-way from the equator to the north pole, a harvest 
moon ordinarily rises only about a quarter of an hour later, 
while a full moon in spring rises about one hour and a quarter 

r. than on the previous evening. By means of the expla- 
nations already given, we might follow out the apparent move- 
ments of the Moon at various times of a lunation occurring 
at any season of the year ; but these movements do not 
require any description in a work of this kind. 

342. The apparent movements of Venus and Mercury are 
by turns direct and retrograde, carrying these planets past 
the Sun from one elongation to the other (332). An inferior 
planet has an apparent retrograde movement when passing 
between the Earth and Sun ; that is, its movement from its 
eastern I -tern elongation carries it through its inferior 

conjunction ; while its movement from the west to the east of 
the Sun carries it through its superior conjunction. When 

gation, so as to be visible for a 
time after sunset, it is usually called the evening star; and 
:n in the morning near its western elongation it is 
called the morn: ie times it is far brighter 

than any celestial object except the Sun and Moon, and gives 
linct shadows on any smooth white 
surface. It may often be plainly seen while the Sun is above 
the horizon. It i.^ brightest, as has been said, a little after 



190 Outlines of Astronomy. [Sec. 342. 

its eastern or a little before its western elongation (333), 
when it appears as a crescent in the telescope. The horns 
of this crescent seem extended farther round the disk than 
they would reach by means of irradiation alone ; this exten- 
sion is thought to be due to refraction in the planet's atmos- 
phere. 

343. Within the crescent formed by the illuminated portion 
of the disk of Venus, the rest of the disk is sometimes visible, 
like that of the new moon (193). How this happens is not 
known ; for Venus is never near enough to the Earth to 
much reflected sunlight from it. as the Moon does. [{ 
possible that some light like that of the terrestrial aurora 
may at times be shining in the atmosphere of Venus; but 
this is nothing more than one of tin 3 which have been 
made about the appearance just described, although it 
more likely guess than that of one astronomer, who thought 
that Venus might be inhabited by people who had a custom 
of lighting bonfires occasionally all over their planet 

344. The names of morning and evening star are sometimes 
given to Mercury, and even to some of the superior planets, 
as well as to Venus ; but Mercury is a planet seldom noticed at 
all, being generally too nearly in a line with the Sun to be 
visible. When it can be seen, it appears like a rather bright 
star. 

345. The apparent movements of the superior planets along 
the zodiac are direct, except when the Earth passes nearly 
between the Sun and one of these planets, so as to bring it 
into opposition. At such times the planet has an apparent 
retrograde movement, due to the facts that its real direct 
movement is slower than that of the Earth, and that the 
Earth's movement is almost directly across the line join- 
ing the planet and the Sun. Any superior planet, about the 
time of its opposition, will apparently retrograde farther, but 
will occupy fewer days in retrograding, than will any planet 
much more distant from the Sun, and therefore from the 
Earth. Hence Mars, the nearest of the superior planets, 
has a remarkably unsteady apparent movement ; retrograding 



Sec. 345.] Phenomena. 191 

rapidly for a comparatively short time, and at other times 
changing the rate of its direct movement considerably in 
different parts of the zodiac. These effects are often in- 
creased by the considerable eccentricity of its orbit ; so 
that before the discovery of Kepler's laws its movements 
were thought very perplexing, and could not well be ac- 
counted for by any theory of the Solar System that had 
been contrived. 

346. The apparent direct motion of a superior planet can- 
not ordinarily be as quick as the apparent direct movement 
of the Sun ; so that at the time of the conjunction of the 
planet the Sun apparently overtakes and passes it. The 
times oi day at which any planet rises and sets during any 

sod depend, of course, on its place at that season in the 
zodiac ; the explanations already given with regard to the 
Sun and Moon will be sufficient to account for the appear- 
ances occasioned by such movements of the planets as can be 
observed without astronomical instruments. 

347. The appearances called transits, eclipses, and occul- 
tations, still remain to be noticed. These are all due to the 

of one celestial object directly between two others, 
and ma}- all be illustrated by some such comparison as the 
following. 

348. If a man is walking past some large building, at a 
considerable distance from it, while carriages are occasionally 
passing between him and the building, they will hide more or 
less of it from him as they pass, according to their distance 
from him and their size. A small carriage passing within a 

feet of him may hide the whole length of the building for 
a second or two ; while a still larger carriage driven close by 
the building will appear to cover only a small part of it at 
once. If a low carriage or an open wagon passes between 
the observer and the building, he may be able to see the 
upper part of the building over the carriage, even if it passes 
near him. 

M9i Any particular carriage, then, will hide more of the 
building the nearer it pa.^se.^ to the observer. But it will take 



192 Outlines of Astronomy. [Sec. 349. 

longer to pass in front of the building the farther it passes 
from the observer. Suppose two straight lines drawn from 
the observer, one to each end of the building. Then a car- 
riage will begin to hide the building as soon as it begins to 
cross the first of these lines to which it comes, and will ( 
tinue to hide some part of the building until it has entirely 
crossed the second line. But the space it has to cross from 
one line to the other is greater the farther it is from the 
observer. If it is not driven directly across this space, it 
will usually be longer between the lines than it would be if it 
crossed both of them equally far from the observer ; but if 
its course carries it partly towards him, it will come to the 
Ond line at a place where the two lini :her 

than they were at the place where it Crossed the first line ; 
that its cour.se between the lines may be no longer, or may 
even be shorter than if it had crossed them both equally far 
from the observer. 

350. If the observer, as we supposed at first, is hi' 
moving along while the carriage passes, the two lines will be 
always shifting their places. This will make a difference in 
the particular time at which the carriage will cross eitlu : 
them ; but it will not make any difference in tin era! 
rules that the carriage hides more of the building at a time the 
nearer it is to the observer, and continues to hide one part or 
another of the building for a longer time the farther it is from 
the observer. Of Course, if the carriage and tin are 
moving Contrary ways, it will not be so long between him and 
the building as it would be if it moved the same way with 
him. 

351. There is another way of looking at the same facts. 
Suppose it to be evening and that the building is illuminated. 
We may wish to inquire how much ground will be covered 
by the shadow of the carriage. In order to distinguish 
tween the ends of the building, we will call them north and 
south ends, considering the building as facing eastwards. 
Then if a line is drawn from the northernmost light in the 
building past the northern edge of the carriage, and from the 



Sec. 351.] Phenomena. 193 

southernmost light in the building past the southern edge of 
the carnage, the place where these lines cross, beyond the 
carriage, will be as far as its shadow reaches. Anywhere 
between these lines, and between the place where they cross 
and the carriage, the carriage cuts off the view of both the 
northernmost and the southernmost light at once. Outside 
of this space, one light at least will not be behind the car- 
riage. 

&»2« But if we wish to know the shape of the space from 
which the carriage hides some of the lights in the building, 
we mav suppose lines drawn from all the lights near the ends 
and top of the building, so that each line touches the carriage 
on the edge farthest from the light it starts from. For in- 
stance, let a line be drawn from the northernmost light to the 
southern edge of the carriage and from the southernmost 
light to the northern edge of the carriage. These lines will 
cross or come nearest to each other between the building 
and the carriage, and will get continually farther apart beyond 
the carriage ; so that the farther off we are the more space 
there will be within which some of the light from the building 
is cut off by the carriage. 

353. When a dark object, like the Moon or a planet, is 
considered as lighted up by the Sun on one side and casting 
a shadow on the other, the shadow itself is called an umbra, 
and the space behind the planet from which it cuts off some 
sunlight is called a penumbra. In this sense, the words 
umbra and penumbra have a very different meaning from 
that which they have when used with regard to the solar 
spots (56). 

3->l. Since the planets are smaller than the Sun, and are 
globular, their umbrae are funnel-shaped. From the place 
where an umbra ends, the planet to which it belongs must 
look just as large as the Sun ; from any place within the 
umbra the planet must look larger than the Sun ; and from 
any place beyond the end of the umbra the Sun must look 
larger than the planet (267). If we take a glass funnel and 
fit two round flat pieces of pasteboard into it, one larger than 

13 



EXPLANATION OF PLATE IX. 

In this plate, the dot at E represents the Earth on about the 
same scale as that on which the Sun la represented in ri.it- 

page 38. The width of the Barth's orbit, on the Bame BCale, is about 

equal to the joint length of a number of linea of print, one from 

each page between I'l.ites Land IX. By taking one line from' 

leaf only, we shall accordingly have the distance of the Earth from 
the Sun. The corresponding extent of the penumbra <>f Mercury 

and Venus, at the distance of the Earth from the Sun, is also 
shown in Plate IX. 



Errata. — Owing t«. an error in the printing of this editi 

XI , and XII have been placed between pages 193 and -f between 

pages 207 and soS. Tin- number I I I and IX. should be 

about 170. in order U) make the explanation of Plate IX. correct. 



PLATE IX. 



Limit o{ Mercury's penumbra. 



MO represent part of the Moon's orbit. If the Moon is at M, its 
umbra extends to U. 



M 



Penumbra of the Moon. 



Limit of the penumbra of Venus. 



Umbra of the Earth. 



Limit of the penumbra of Venus. 



Limit of Mercury's penumbra. 



EXPLANATION OF PLATE X. 

The figures of Plate X. shorn orthographic projections (270) of 
the Tropica and Polai and may be compared with the 

projections shown in Plate X I. Why is the spot marking the pi 
of the pole, in the upper figure, out of the centre of the ellipse 
representing the Antic or Antai } It we regard this 

pole as the south pole, is it the time of sunrise or of sunset in that 
part of the Earth which occupies the centre of the upper figure? 
In the lower figure, it we suppose Norway to be at the top, is it 

sunrise or sunset there? On the same supposition, what part of 

the Earth at this time has the Sun in its zenith ? and what is the 
season of the year, spring or autumn ? 



PLATE X. 

DISTRIBUTION OF LIGHT AT AX EQUINOX. 

See Sections 270, 29:, 299. 




EXPLANATION OF PLATE XI. 

The figures of Plate XI., like those of Plate X.. show ortho- 
graphic projections of the Tropics and Polar Circles. Numerous 
questions, like those given with Plate X., may be asked with regard 

to this Plate, and answered with the aid oi an atlas. 



PLATE XI. 
DISTRIBUTION OF LIGHT AT A SOLSTICE. 

See Sections 270, 295, 299. 





EXPLANATION OF PLATE XII. 

The parallel lines shown in Plate XII. may be supposed to lie 
on a rounded surface, so that they are not all in one plane. The 
two lines AC and I5D, at right angles with each other, arc per- 
pendicular to each other, whether we hold one of them vertical, 
or not. 

The circle AGDBEH may be understood to represent the 
intersection of a Sphere with the plane of the paper. The sphere 

has its centre at C in the plane of the paper, and is orthographi- 

cally projected on that plane (-~o), the point of Sight being Indefi- 
nitely distant, and in a line drawn through < perpendicular to the 

plane of the paper. Heme AGDBEH i> a great circle of the 

sphere, and appears as a circle. Ar.y other great circle mtlSt 
appear as an ellipse or straight line. The line AB may In 
garded as a diameter of the Sphl I 
circle the plane of which is perpendicular to the plane of the 

paper. The half ellipse APFLB will represent halt 

circle. The circles TMN, PQR, are Small circles in pla 
parallel to the plane of the paper. The ellipse RSQ represent! 

a small circle the plane of which is inclined to that of the pa] 
and GTFH, which is more than half an ellip entS part 

of a small circle, since its major axis docs not pa^> through C 
A line drawn from the middle of its major axis through C would 
be perpendicular to its major axis. If this were not the l 
would the ellipse represent a circle of the sphere? Are both 
ADL and AGF spherical triangles ? To what curve is the straight 
line AH tangent ? 

In each of the two cones, the line AB IS the axis of tin 
tion by which the cone is formed, and CD the rotating line. The 
shape, though not the kind, of any conic section, will obvi<> 
vary according to the angle between AB and CD, as well as with 
the angle between AB and the intersecting plane. 



PLATE XII. 

GEOMETRICAL FIGURES. 

Srr Sections 396, 402, 412, 414, 41S, 4 22 

c 




194 Outlines of Astronomy. [Sec. 354. 

the other, and nearer the mouth of the funnel, the two pieces 
must look equally large from the place where the sides of the 
funnel come together ; for the smaller piece would appear 
from that place just to hide the larger piece ; and that place 
would be the end of the shadow of the smaller piece of paste- 
board if the larger piece were luminous. 

355. The penumbra of a planet takes in more and more 
space the farther it reaches ; and the farther away from the 
planet is the place in this penumbra from which we may 
suppose ourselves to be looking, the smaller the planet must 
look compared with the Sun ; although both the Sun and the 
planet must look smaller than from a place nearer to them. 

356. Mercury is a little larger than the Moon (195); but 
the Moon looks about as large as the Sun, while Mercury 
has only a small disk when examined with a telescope. 
Hence, when the Moon comes between us and the Sun. its 
umbra reaches about as tar as the Earth : and it may hide 
the Sun for a lew minutes at a time, while Mercury looks like 
a small black spot when it is seen upon the Sun's disk. On 
the other hand, the penumbra of Mercury, where we 

has spread out far enough to take in a row of many more 
than a hundred such bodies as the Earth ; while the width 
of the Moon's penumbra, where we cross it. is only about half 
the length of the Earth's diameter. Accordingly, when Mer- 
cury can be seen on the Sun's disk from any part of the 
Earth, it will be seen there from all parts of the Earth where 
the Sun is then above the horizon, unless the Earth is just 
grazing the penumbra of Mercury. Hut when the Earth 
crosses the Moon's penumbra, there will still be terrestrial 
places from which the full disk of the Sun will be visible. 
That is, although the Moon is large enough to cover the 
whole Sun at certain times, yet if we could travel about 
quickly enough on the Earth, we could apparently shift the 
Moon from one side of the Sun to the other by our own 
movements, at times when its centre was nearly between 
those of the Sun and the Earth. But when Mercury is 
between us and the Sun, the most that we could do by 



Sec. 356.] Phenomena. 195 

moving about on the Earth would be very slightly to shift the 
place of the planet on the Sun's disk. Still another state- 

.: of the same Tacts would be that the parallax of the 

■n, as compared with the Sun's parallax, is larger than 
the parallax of Mercury as compared with that of the Sun. 

the appearances due to parallax are very familiar, the 
•word may be partly explained without the use of mathemati- 
cal terms. 

357. If we look through a window at distant objects, we 

see that the place oi the bars of the window-frame can be 

considerably, with regard to the objects 

ind them, by small movements of our own. But we must 
walk a Ion:; way before we can thus change the apparent 
a distant house with respect to the landscape behind 
it. irent change of place of this kind may be called 

the parallax of the object observed as compared with the 
. of the objects behind it ; for these objects must also 
S tly displaced, by our movements, with respect to other 
objects still farther from us. Since the amount of the paral- 
lax of an object depends in some way on its distance from 

we may naturally suppose that ite distance can be found 
out by means of its parallax ; and this is actually the case. 
o measurements of parallax can be perfectly exact, 
the distance of a remote object is not easily found. Mistakes 
in the measurement of its parallax will occasion a greater 
uncertainty as to its distance than will be occasioned with 

ect to the distance of a near object by mistakes equally 
ge in the observations made upon it. So far as the dis- 
tance of ai ts beyond the Solar System has been 
determined, the determination depends upon apparent move- 
ments of these objects due to the Earth's motion in its orbit. 
The mean distances of the planets (147), and hence our dis- 
tance from the Sun, are learned by observing the parallax 
of any one planet as compared with that of stars nearly in a 
line with it, or with that of the Sun. This parallax does not 
depend on the Earth's movement in its orbit, but only on the 
different views of the planets which we have from different 
par* Earth. 



196 Outlines of Astronomy. . 358. 

358. When the actual distance from the Earth- of any 
planet at any particular time has been learned, the mean 
tances of all the planets may be learned by observing the 
periods of their revolutions about the Sun ; for these periods 
are connected with the comparative distances of the planets 
by Kepler's third law (150); or, more strictly speaking, by 
the general laws of motion. The Moon's parallax, and tli 
fore its distance, can be more easily determined than those 
of any other celestial object ; and one way of determining the 
distances of the Sun and other objects belonging to the Solar 
Svstem consists in calculations depending on the Mo 
distance and movements; but more direct and sat: 
methods of finding the Sun's distance are furnished by ol - 
vations of Venus and Mars. At the time of its inferior I 
junction (328), Venus cornea nearer to the Earth than 
other of the principal planets If it can then be 

seen, its parallax can be better determined than that of any 
other planet ; but this happens only at those interior conjunc- 
tions when it is so close to the plane of the ecliptic that the 
Earth enters its penumbra. Transits ofVenus | 
dom seen, but usually occur in pairs, the time between the 
two transits of each pair being only eight years. The \- 
of the eighteenth century marked by transits of Wnus v. 
1761 and 1769 : those of this century are 1X74 and 1SS2 ; the 
next transits will not occur till the years 2004 and 2012. 

359. Mars, at its oppositions, con. enough to the 
Earth to make observations of its parallax practicable ; and 
our knowledge of the distances among the bodies of the 
Solar System depends to a great extent on the numerous 
observations which have been made upon Mars, especially at 
those oppositions when Mars and the Earth are unusually 
near each other (200). 

360. The transits of Mercury are much more frequent 
than those of Venus ; but Mercury is too far from us to 
allow its parallax to be very accurately determined by direct 
observation. 

361. The passage of any object across another, or across 



Sec. 361.] Phenomena. 197 

a boundary of any kind, may be called a transit ; and many 

ronomical events ot very different kinds are in fact called 

transits. The only transits, except those of Venus and 

Mercury across the Sun's disk, which we need consider at 

present, are those of satellites across the disks of the planets 

to which they belong. The frequency of the transits of 

Jupiter's satellites has already been mentioned (207). The 

ot the shadow of any satellite of Jupiter across the 

planet's disk is often called a transit of the shadow ; it is an 

,t of the same kind with those called eclipses of the Sun, 

which are due to the Moon's shadow upon the Earth. 

An occultation is the hiding of an apparently small 
body behind some other moving object. Jupiter's satellites 
are frequently occulted by Jupiter; stars and planets are 
often occulted by the Moon, and sometimes by planets. The 
occultation of any celestial object behind the Sun could not 
be 1 -hould lose sight of the object while it 

- still apparently at a considerable distance from the Sun. 
Occultations of stars by the Moon can seldom be observed 
without the help of some instrument ; but many can be dis- 
tinctly seen with a spy-glass or an opera-glass. The disap- 
pearance of the star behind the Moon is called its immersion, 
and )earance is called its emersion. Immersions 

take place on the following limb of the Moon (49, 183), and 
m new moon to full moon, on the dark limb. 
en the dark limb is too feebly lighted to be visible at all, 
3 over which it passes seem, at their immersions, to 
be extinguished without any obvious reason and with sur- 
prising suddenness. Emersions from behind the Moon's 
dark limb may be seen after the time of full moon ; but the 
moment when the star is to appear has first to be calculated, 
e do not know when to look for its emersion. Immer- 
s and emersions on the bright limb arc less interesting 
than those on the dark limb. At their immersions on the 
.lit limb, stars occasionally seem to come a little within 
the limb before they disappear. This appearance is probably 
due tu some optical illusion not yet clearly explained. 



198 Outlines of Astronomy. [Sec. 363. 

363. The Moon is so much displaced among the stars by 
the effect of parallax that a star seen, for example, a little 
south of the Moon, near the equator, must appear north of it 
in the north frigid zone. Hence a star occulted by the Moon 
at one terrestrial place may escape occultation at another not 
very remote from it. 

3G4, A satellite is said to be eclipsed when it is in the 
umbra of the planet to which it belongs ; and the Sun is said 
to be eclipsed when its light is partly or wholly cut off from 

us by the Moon. Eclipses of the satellites of Jupiter are i 

frequent ; in fact, the first, second, and third of these satel- 
lites (20X) are eclipsed every time they go round the planet 
The fourth satellite, also, is usually eclipsed at each n 
lution; but it sometimes ; 1 the planet's urn 

although the extent of this umbra must be nearly as great at 

the distance of the fourth satellite as it is at any place, on 
account of Jupiter's great size and distance from the Sun. 

But the orbit oi the fourth satellite does not lie quite 
nearly in the plane of Jupiter's orbit the 

other satellites. 

X<>.~>. When Jupiter is in opposition, its shadow and the 
shadows of its satellites point nearly away from the Earth. 
In this case, the satellites must go Dearly behind the plai 
as seen from the Earth, whenever they are eelipsed ; and anv 
Satellite which casts a shadow on Jupiter must itself be nearly 
between Jupiter and the Earth. Hut this is not the case when 

Jupiter is at one of its quadratures. Suppose, for example, 

that Jupiter is high in the sky at sunset. Then its shai 
and those of its satellites must be cast eastwards with res; 
to the terrestrial place of observation ; so that a satellite the 
shadow of which is on Jupiter will be a little west of the 
planet ; and an eclipsed satellite will be a little east of 
Jupiter, so that its reappearance after the eclipse can 
observed, even if its disappearance took place behind the 
planet. But it often happens that both the disappearance 
and the reappearance of a satellite of Jupiter may be ob- 
served. 



Sec. 366.] Phenomena. 199 

366. The shadow of Saturn's ring on the ball or of the ball 
on the ring constitutes what may be called an eclipse. But the 
changes of these appearances are too slow to make them like 
eclipses in the ordinary sense of the word. The eclipses 
occasioned by the movements of Saturn's satellites occur 
comparatively seldom, owing to the considerable inclination 
of the orbits of these satellites to the plane of Saturn's 
orbit. 

307. The Moon is not eclipsed very often ; for, owing to 
the inclination oi its orbit, it is often out of the plane of the 
ecliptic when it comes into opposition, so that it passes on 
one side or the other of the Earth's umbra, which is of course 
much smaller than Jupiter's umbra, though large compared 
the Moon, so that the Moon may continue wholly 
eclipsed for about two hours at a time, while it is passing 
through the umbra of the Earth. The Moon is sometimes 
only partially eclipsed : that is, some part of its disk is near 
enough to the plane of the ecliptic to be eclipsed at one of its 
oppositions while the rest of the disk passes outside of the 
Earth's umbra. When the whole disk of the Moon is eclipsed, 
the eclipse is total, or is in its total phase. Before and after 
the tota! phase, there must of course be partial phases of the 
eclipse as the Moon gradually enters and leaves the shadow. 

:><»V Even when the Moon is farthest within the" shadow 
of the Earth, its disk is still visible: for one of the effects of 
refraction occasioned by the Earth's atmosphere (262) is to 
send a little sunlight into some parts of the region from which 
e Sun is cut off by the Earth. Refraction 
not only turns light out of its course, but separates it into 
light of different ind the middle of that part of the 

rth's umbra crossed by the Moon contains a little reddish 

>r of which is due partly to refraction and partly 

Hence the disk of the eclipsed Moon usually 

appears a dull red. The colors of the Sun and Moon seen 

near the horizon, and not eclipsed, are due to absorption 

ii<»t>. One effect of refraction is to increase the indistinct- 



200 Outlines of Astronomy. [Sec. 369. 

ness of the boundaries of the Earth's shadow, so that it is 
hard to tell when the Moon first touches this shadow at the 
beginning or leaves it at the close of an eclipse. 

370. When the Moon is within the penumbra, but not 
within the umbra of the Earth, some light is cut off from it, 
but not enough to darken it so much that it can then be con- 
sidered as eclipsed. But from any part of the Earth which is 
within the Moon's penumbra, the disk of the Sun is not 
wholly visible, some part of it being behind the Moon ; and 
thus what is called a partial eclipse of the Sun takes p] 
Eclipses of the Sun, then, must be more frequent than 
eclipses of the Moon ; for an eclipse of the Moon is not 
considered as occurring unless the Moon touches the Earth's 
Umbra, while an eclipse of the Sun is considered as occur- 
ring whenever the Moon's penumbra touches the Earth. 

There must be at Least two, and there may be five, eclij 

of the Sun in the course of a year ; while there may be no 
eclipses of the Moon in the course of a year, and cannot be 
more than three. Seven eclipses, live of the Sun and two 
of the Moon, or four of the Sun and three of the Moon, are 
as many as can happen in the course of a year. But we 
more eclipses of the Moon than of the Sun from any one 
terrestrial place ; for an eclipse of the Moon must be visible 
from any place on the Earth from which the Moon can be 
seen at all ; but the Sun may be eclipsed at one place while 
its whole disk can be seen from another (356). The various 
periodical movements of the Moon and of the Earth bring 
them at every moment into nearly the same situation with 
respect to each other and to the Sun which they occupied 
about eighteen years, or more exactly, two hundred and 
twenty-three lunations, before. Hence the eclipses which 
occur during every two hundred and twenty-three lunations 
occur in a like order with those of the two hundred and 
twenty-three previous lunations, but differ from them to some 
extent in their appearance. 

371. An eclipse of the Sun is central at any place across 
the line between which and the centre of the Sun the Moon's 



Sec. 371.] Phenomena. 201 

centre is passing. An eclipse of the Sun which is nearly 
central is total, or is in its total phase, if the umbra of the 
Moon reaches the Earth, in which case the Moon cannot 
look smaller and may look larger than the Sun (354) as seen 
from the place where the eclipse is observed ; so that the 
>k of the Sun will be hidden. But if the Moon is 
near apogee (177) at the time of the eclipse, its umbra will 
not reach as far as the Earth, and it will look smaller than 
the Sun. Hence the limb of the Sun will be seen all round 
the disk oi the Moon at places where the eclipse is nearly 
central, and the eclipse will be annular, or in its annular 
phase. When an eclipse of the Sun is not nearly enough 

ral to be either total or annular, it is called partial, or 
said to be in a partial phase at any particular time and place. 
TIk I time which the total phase of any eclipse of the 

Sun may last at any particular terrestrial place is near eight 
minutes ; but this can only happen when the Earth is near 
aphelion, so that the Sun looks about as small as it ever does, 
the Moon near perigee, so that it looks about as large as it 
ever does, and the place of observation on the equator, where 
the Earth's rotation helps as much as possible to prolong the 
eclipse. A total eclipse, along the line where it is central, 
seldom lasts longer than five minutes in any one place ; and 

length varies a good deal at different parts of the line 

central. Since all parts of the Earth are not 

equilly distant from the Moon, an eclipse may be total at 

one place on this central line and yet appear as an annular 

eclipse when it passes another place farther from the Moon. 

The place on the Earth nearest the Moon at any particular 

time is of course that through the zenith of which the Moon 

is then | At the time of an ec.ipse of the Sun, the ter- 

the Moon is also nearest the Sun ; but 

the Sun is too far off for its apparent size to be changed as 

much as is that of the Moon by a change of the place of 

"ion from one part of the Eartli to another. Some 

people fancy that both the Moon and Sun look larger when 

horizon than when they are high in the sky. 



zo2 Outlines of Astronomy. [Sec. 371. 

This mistake comes from the fact that when the Sun or the 
Moon is near the horizon it can be better compared with 
distant terrestrial objects than when it is high in the sky. In 
fact, the Sun looks about as large at one height as at another, 
and the Moon looks largest when it is highest. But the 
apparent size of the Sun and of the Moon varies noticeably 
according to the variation of the distances between them and 
the Earth. The greatest magnitude of an eclipse either of 
the Sun or Moon was formerly stated by dividing the disk 
of the eclipsed object into twelve parts, called digits, and 
naming the number of digits eclipsed ; but it is now usual to 
state the eclipsed fraction of the di.sk more precisely than 
can thus be done. 

87$« Even when the Moon ifl nearest to the Earth at the 
time of a total eclipse of the Sun. its umbra is redm 
width of less than two hundred miles before it reaches the 
Earth. Hence the Sun cannot be totally eclip- r the 

whole at onre of a very larg a ; and the entire 

track of a total eclipse of the Sun usual'; I only a small 

fraction of the Earth. Since a large part of the Earth is 
covered by water, and much of the land is uninhabited, it 
is not surprising that a total eclipse of the Sun is seldom 
witnessed. 

#7#. When the Sun is totally eclipsed, the corona (73) 
and any large prominent. ,) which may then be on 

the limb of the Sun can be seen without the help of any 
instrument. The foim, brightness, color, and apparent size 
of the corona have been very differently described by different 
observers, so that we can hardly 1 * how the corona 

usually looks, and cannot say at all whv it looks as it does. 
The total phase of an eclipse of the Sun lasts so short a time 
at any place, and presents so many strange and interes- 
appearances, that the spectators of it can hardly notice any 
thing distinctly before it is over. But accurate observers, 
each attending only to one appearance, and neglecting all 
the others, have succeeded, after all, in obtaining much more 
information during the total phases of recent eclipses than 
would have been expected. 



TOTAL ECI 



Plate VIII. 




This view is copied from a photograph. It shows the corona and 
prominences. The apparent indentations on the Moon's limb under 
the prominences are due to the prolonged exposure of the photographic 
plate which was necessary to secure a view of the corona. 



Sec. 374.] Phenomena. 203 

374. During a total eclipse of the Sun, the darkness is 
about as great as it is a few minutes after sunset; and the 
arrangement of the clouds in the sky at the time makes much 
difference in the amount of the darkness when the Sun is 
concealed, either by the Moon, or by the Earth itself just 
after sunset. Several ot the brightest stars and planets may 
usually be seen while the Sun is totally eclipsed. The Moon 
itself is faintly illuminated at such times by sunlight reflected 
from the parts of the Earth outside of the Moon's shadow ; 
and it has been thought that the different tints which the 
Moon has seemed to have at the times of different eclipses 
may be due to the differences which there must be between 
the light reflected from one part of the Earth and from an- 
other. When the Pacific Ocean, for instance, faces the Sun 
and Moon, the Moon's color may be expected to differ from 
that which it will have when illuminated by light reflected 
from the continent of Asia. The Moon looks globular to 
some observers when seen against the coronal light ; this 
may be due to the effects of light and shade produced on it 
by reflected light from the Earth. 

The light by which terrestrial objects are seen during 
a total eclipse of the Sun is generally reported to be some- 
what unlike ordinary twilight. This may naturally be the 
. since the effects of refraction, absorption, and reflection, 
to which this light is due, must usually differ from those 
which produce twilight. Animals are sometimes frightened 
by a total eclipse of the Sun, but more commonly act as 
though they supposed the Sun to have set in the usual way. 
i Poultry, for example, go to roost, and cattle return to their 
The daylight seems gradually to diminish before 
the total phase of ?n eclipse of the Sun; but the instant the 
Sun begins to reappear, the full brightness of daylight seems 
to return. In like manner, we notice the gradual lessening 
of the daylight before sunset, but not its increase after sun- 

376. Just before and after the total phase of an eclipse, 
the Moon's shadow may sometimes be notiu ing rap- 



204 Outlines of Astronomy. [Sec. 376. 

idly over the landscape ; and singular wavy lines of light and 
shade appear upon the ground, the cause of which has not 
been determined. 

377. While an eclipse of the Sun is in its partial phase, 
the part of the Sun's disk not yet hidden appears as a < 
cent of greater or less width. When the crescent is very 
narrow, just before or after the total phase of the eclipse, it 
often appears to be broken up into detached portions. This 
effect is considered to be due to the uneven ness of the 
Moon's limb, and to be increased by irradiation. The ap- 
pearance goes by the name of Baily's Beads, Baily being the 
name of an astronomer who called attention to this breaking 
up of the Sun's limb. 

378. A tew extracts may lure be given from the numerous 
reports made upon the total eclipse visible in the central 
parts of the United States on AtlgUSl 7. 1 869. 

379. At Shelbyville, Kentucky, ling to Mr. Blake, 
"about twenty-eight minutes before totality ... I noticed 

that shadows were quite indistinct ; that the air was gro? 
chilly ; and that the sunlight gave a peculiarly gloomy aspect 
to the landscape. 

380. "Thirteen minutes before totality the air felt quite 
cold; the Sun appeared as a beautiful crescent, while the 
black edge of the Moon seemed to stand out from it. gn 
one the idea of a stereoscopic picture. ... I was struck by the 
appearance of the trees to the eastward of the tent, and about 
fifty feet distant ; the foliage was of a peculiar color, very 
similar to that produced by the electric light. . . . 

381. "Eight minutes before totality, the limbs of the Sun 
and Moon were shaking violently, and the sunlight 
diminished to such an extent that the faces of the obsen 
were of a livid hue, not unlike that of a corpse. Facing to 
the eastward, I saw that the southern edge of my shai 
was comparatively sharp and distinct, while the northern edge 
was ill-defined and very faint. . . . 

382. "The corona, of which, up to this moment'' (that of 
the beginning of the total phase) " there had been positively 



Sec. 382.] Phenomena. 205 

no indications, now appeared as an extremely soft white light, 
surrounding the Sun and extending from it, in all directions, 
to a distance of at least two-thirds of its diameter. There 
was no appearance of rays, nor was there any sparkling 
light. . . . 

3S3. "Simultaneously with the appearance of the corona, 
some of the planets and larger fixed stars became visible 
to the naked eye. They did not appear as they ordinarily do 
at night, but seemed to shine with a very soft and slightly 
diffused white light. The sky, in the vicinity of the Sun, 
was not blue, as at night, but was of a peculiar milky hue ; 
in the zenith it seemed to be of a purplish tinge, and had a 
more gloomy aspect ; the eastern sky was lighted up with 
a lurid glare similar to that which sometimes attends an 
autumn sunset. . . . The darkness was so great that it was 
impossible to distinguish the foliage of trees a ftw rods 
distant." 

384. General Myer saw the eclipse from the summit of 
White Top Mountain, in Virginia. According to his account 
of the appearances noticed during the total phase, — 

" As a centre stood the full and intensely black disk of the 
Moon, surrounded by the aureola of a soft bright light, through 
which shot out as if from the circumference of the Moon 
straight massive silvery rays, seeming distinct and separate 
from each other, to a distance of two or three diameters of the 
lunar disk ; the whole spectacle showing as upon a background 
of diffused rose-colored light. This light was most intense 
and extended furthest at about the centre of the lower limb, the 
position of the southern prominence. The silvery rays were 
longest and most prominent at four points of the circum- 
ference, two upon the upper and two upon the lower portion. 
. . . These discrete rays were not visible to me, or did not 
attract my attention, with the telescope, and the diffused rose- 
colored light seemed to resolve itself in the field of the glass 
into the prominences. . . . The sight presented to the unaided 
eye was the superior in beauty ; that through the glass in 
interest. This was so markedly the case that there was a 



206 Outlines of Astronomy. [Sec. 384. 

sense of disappointment, on resorting to the telescope, at 
rinding the size and beauty of the spectacle, as seen by the 
naked eye, so much reduced by the definition of the glass. 

385. " The approach of the Moon's shadow did not appear 
to be marked by any defined line, or movement of any dark 
column of shade through the air. The darkness fell grad- 
ually, shrouding the mountain ranges and the dim world 
below in most impressive gloom. Our guides had been 
instructed to watch for the shadow as described, and to call 
to us at the glasses. They saw nothing of which to g 
notice. At the same time, and in vivid contrast, the clouds 
above the horizon were illuminated with a soft radiai 
those towards the east with lights like those of a coming 
dawn, orange and rose prevailing ; those northward and 
westward, as described to us by Mr. Charles Coale, of 
Abingdon, Virginia, who was present, with rainbow bands 
of light of varied hues." 

386. Mr. Coale'fl account of this appearance is as fol- 
lows : — 

" Those who have had the privilege of bring upon White 
Top, and enjoying the westward scene, will remember the 
grand panoramic view of mountains beginning on the north- 
ern and southern horizon, and stretching away to the * 
till they seem to meet. . . . Stretching along this semi- 
circle of mountains, in long horizontal lines, far below 
the Sun, lay light and fleecy clouds. ... At the moment 
of the falling of the dark shadow, when naught was to 
be seen above but the stars and the circle of light around 
the Moon, these clouds became arrayed in all the colors of 
the rainbow." 

387. In a letter afterwards written, Mr. Coale says with 
reference to the preceding description: — 

" I distinctly remember that there were distinct bands of 
pink, purple, yellow, orange, and fiery red, and each slightly 
tinged with different shades of its own color. One of the 
bands, I remember, had to my vision a slight lilac tinge. I 
do not remember to have observed any green or blue, but 



Sec. 3S7.] Phenomena. 207 

I do remember that the lower edge of the purple had a very 
faint blue tinge." 

3SS. From the preceding accounts we may readily per- 
ceive that, when seen under favorable circumstances, the 
total phase of an eclipse of the Sun presents appearances 
like those of a fine sunset or sunrise, in addition to the 
peculiarly interesting spectacles afforded by the dark disk of 
the Moon surrounded by the light of the Sun's corona, and 
by the character of the light scattered through the atmos- 
phere around the spectator (375). General Myer's remark, 
that the use of a telescope lessened the beauty of the appear- 
ances seen without one, is generally applicable to astronomi- 
cal appearances, almost without exception. Telescopes are 
useful means of acquiring knowledge, when used by persons 
who understand how to use them to good advantage ; but 
they add little or nothing to the grandeur and beauty of the 
sky and the stars. Those who imagine that wonderful sights 
are constantly to be enjoyed by means of astronomical instru- 
ments, fail to comprehend what those instruments are made 
for. To explain this will be one of the chief objects of the 
following chapters. 



2o8 Outlines of Astronomy. [Sec. 389. 



CHAPTER VIII. 

GEOMETRICAL TERMS. 

389. Our attention has thus far been mainly directed to 
various opinions respecting the objects which make up the 
universe, many of these opinions being firmly established, 
while others are still under examination by astronon, 
To understand how any of them have been formed, we D 
know something of geometry, of optics, and of the technical 
terms used in practical astronomy. 

390. The object of geometry is the measurement of 
material objects, or the study of their sizes and shapes. It 
makes no ditference in the geometrical study of any object 
whether this object is a solid, a Liquid, or a gas ; whiclx 

it is, it may be called a geometrical solid. The weigl 
and chemical properties of all objects are also left OUt 
when the objects are regarded as geometrical solids. A g 
metrical solid, then, is whatever takes up any any 

part of space, in fact, may be called a geometrical solid, even 
if it contains no matter. 

391. Now if a geometrical solid is cut in two, there is some- 
thing belonging at once to both of its parts which has shape 
and size, and yet which does not add any thing to the size of 
those parts ; for they are no larger, when taken together, than 
the solid from which they were made. This something 
called a surface. We are sometimes reminded that the finest 
statues ever made were already in the blocks of marble from 
which they were cut, before their sculptors began to make 
them. In other words, all that is important about a statue 
is its surface ; nobody can make a new material object, but a 
new surface can easily be made, although it is not easy to 
make one that is beautiful. The space round any material 
object may be considered as part of a geometrical solid of 



Sec. 391.] Geometrical Terms. 209 

which the object itself is another part. The surface of the 

set is the partition between these parts. We have seen 

• every plane may be regarded as a partition dividing the 

universe into two parts (137) ; and a plane is one kind of 

surface. 

3 _\ A surface, then, is whatever may be regarded as divid- 
eometrical solid into parts, without being itself a 
metrical solid. Cut a surface, like a solid, may be cut 
md the boundaries between these parts are called 
lines. So. too, a line may be cut into parts; and these parts 
are marked off from each other by points. A point cannot 
be divided into parts ; that is, it has no size of any kind ; it 
is only the end of a line, or of part of a line. Any surface, 
line, or point, is said to be common to the two solids, sur- 
faces, or lines, which it marks off from each other. 

393. Whenever a body moves, any point which we may 
please to imagine in it goes along some line ; so that, 
although no number of points could be put together so as to 
make a line, no matter how short, yet no point can move 
without going through the whole of some line. This is a sort 
of puzzle, or paradox, as it is called, the explanation of which 
does not belong to mathematics. Mathematicians, however, 
have to contrive some way of suiting their reasonings to the 
facts of nature, and they usually do it by considering every 
moving object as first in one place, then in another close to 
it, and so on, without attending to the passage of the object 
from one place to the next. The places can be supposed 
t<> be as close together as is required by the nature of the 
ject to which any mathematical reasoning may be ap- 
plied. In this way a line may be regarded as a string of 
poi: 

•n a point is regarded as part of a moving body, 
S said to describe the line along which it is carried. In 
like manner, a surface may be described by a line, and a solid 
by a surface. Some lines and surfaces, however, may b< 
moved a ribe nothing beyond themselves. Surf 1 

lines, and points, may of course be considered as moving, 

14 



210 Outlines of Astronomy. [Sec. 394. 

even when we do not take the trouble to suppose a moving 
solid to which the moving surface, line, or point, belongs 
(137). Any number of geometrical solids, surfaces, lines, 
or points may be considered as occupying the same place. 
When two of them occupy exactly the same place, they 
said to coincide ; and even if they do not coincide at the time 
when they are considered, they are said to be equal if they 
might be made to coincide without altering the shape of 
either. If they are not equal, and yet might be made to 
coincide if one of them were first cut into parts and the 
parts all put together again in a new way, they are said to be 
equivalent. 

3<j5 A solid may move so that the line described by 
of its points, or, in other words, by each of the point* we 
please to consider as belonging to it, shall be equal to the 
line described by every other one o\ its points, during .my 

particular part of the movement We 1 .in suppose a n, 

ment of this kind to have been going on and to keep o; 
long as we please, so that the lines described in it have no 
known beginning or end. Let us take a part of one of the 
lines thus described, and move it so that all its points may 
describe equal lines in any given time, and so that it may 
touch others of the original set of lines. If it always DOW? 
cides with some part ol whichever of these lines it tOU< 
as soon as it touches it at all, then all the original lines must 
be what are called straight lines, and the original movement 
must have been of a kind called rectilinear. This explana- 
tion of straightness may seem less comprehensible than 
straightness itself, the meaning of which is seldom doubtful. 
However, the straightness of material objects is actually 
tested by applying them to each other in different w 
The word Straight is frequently omitted in speaking and 
writing; when a line is mentioned, unless we are given to 
understand that it is not straight, we presume it to 1 
straight line. 

396. The straight lines described by the points of a body 
which has rectilinear motion are all said to be parallel to 



Sec. 396.] Geometrical Terms. 211 

each other. All these lines are said to have the direction of 
the movement by which they were described. A body may 
imagined so large as to extend as far every way as we 
please ; and if such a body has a rectilinear movement, its 
points will describe a set of parallel straight lines occupy- 
ing all imaginable places. The rectilinear movements con- 
sidered in geometry are mainly of this kind ; it is to be 
understood that every straight line is as long as we please 
to suppose, so as to have no beginning or end (395), and 
that every point we can name is one of the points belonging 
to some straight line parallel to the first, and having the same 
direction with it : unless we see by what is said about the 
line we are considering that it is only part of a line. Even 
then, a line parallel to it can be drawn through any point we 
choose. 

397. Now, as a matter of fact, no point can be in more than 
one direction from another ; and if any two lines are parallel, 
each is parallel to any line parallel to the other. If the same 
set of parallel straight lines is described by each of two recti- 
linear movements, and the parts of each line are not described 
in the same order in the two movements, although each part 
is described but once in each movement, the directions of 
these movements are opposite. 

398. A direction, then, is that in which a rectilinear move- 
ment, extending through all parts of space which we please 
to imagine, ditFers from every other such movement which 
does not describe the same set of parallel straight lines, 
and describe the parts of each line in the same order. 

399. The notion of direction is commonly taken to be so 
simple that straightness may be explained by means of direc- 
tion. However, to say that a straight line is one everywhere 
having the same direction only amounts to saying that a 
straight line is everywhere straight ; and it may be said that 
a line is still straight if we please to consider the direction of 
one part of it contrary to that of another. But this would be 
only a quibble. 

400. If parallel straight lines are considered as belonging 



212 Outlines of Astronomy. [Sec. 400. 

to the same solid, and this solid has rectilinear movement, 
each of the lines moves along itself, or else they all de- 
scribe surfaces which are called parallel planes. We have 
already considered the meaning of the word plane (137), so 
that we need not say more about it here. 

401. Parallel planes agree in something which is not com- 
monly called direction, because the same set of parallel planes 
may he described by each of a number of rectilinear move- 
ments having different directions. For want of a better 
word some writers say that parallel piai in position. 

ording to this use of the word position, a plane which has 
a rectilinear movement in any direction always keeps the 
same position, however much its place is changed. 

402. If two straight lines are not equal, the whole of one 

must be equal to a part of the other. The lines accordii 

differ in something, which is called length. The distance 
i)i one point from another is the length of the Straight line 
between those points. The distance of a point from any 
other geometrical object is its distance from the point of that 
object nearest to it. If a Straight line is drawn from 
point of a straight line or plane to the nearest point of an- 
other line or plane parallel to the first, it is perpendicular to 
both of the lines or planes it joins ; and if a perpendicular 
is drawn from each of any number of points in one of the 
parallel lines or parallel planes to the other of them, all these 
perpendiculars will be equal. The length of any one per- 
pendicular is called the distance between the parallel lines 
or planes. The word perpendicular is someti: I to 

mean vertical : but a vertical line is perpendicular only to hori- 
zontal lines, and horizontal lines are perpendicular to vertical 
ones. 

403. If a perpendicular is drawn between parallel lines, 
and the lines (or any solids to which we may suppose them 
to belong) rotate about this perpendicular as an axis 
they will describe parallel planes, all of them perpendicular 
to the axis. Planes, then, may be described by a movement 
of rotation as well as by a rectilinear movement (400). 



Sec. 404.] Geometrical Terms. 213 

404. By the rotation of any thing about an axis, it is 
finally brought back to its first position. Hence we can 
divide every whole rotation into parts, which are called 
angles ; but we cannot divide every whole rectilinear move- 
ment into parts called distances, because the movement may 
last so long that no statement of the whole distance it covers 
can be made. However, we may take any part of a recti- 
linear movement, and measure it off into distances on any 
one straight line described by means of it. The size of the 
moving body makes no difference in the distance it moves. 
In like manner, the size of a rotating body makes no differ- 
ence in the angle through which it moves. If an object has 
turned half round about an axis, it has made half a rotation, 
whether it is a grain of sand, the Earth, or an object large 
enough to take in all the known universe. 

405. Two different ways of dividing a rotation into angles 
are in common use in astronomy. The first is to divide a 
rotation into 360 equal angles, called degrees; each degree 
into 60 minutes of arc, and each of these minutes into 60 
seconds of arc. The second way is to divide a rotation into 
24 equal angles, called hours ; each hour into 60 minutes 
of time, and each minute of time into 60 seconds of time. 
Hence, every hour, in this sense of the word, is an angle of 
15 degrees ; every minute of time is an angle of 15 minutes 
of arc, and every second of time is an angle of 15 seconds 
of arc. 

406. For example, T \ of a whole rotation is nearly 32 
decrees. 43 minutes of arc, 38 seconds of arc, and ^ of a 
second of arc; or, as it is usually written, 32 43' 38". 18. 
It is also nearly 2 hours, 10 minutes of time, 54 seconds of 
time, and ftfo of a second of time ; or, as it is usually writ- 
ten. 2 h id 1 54.55 Half a rotation is 180 , or 12*; ] of 
a rotation is 90 , or 6 h ; £ of a rotation is 270°, or 1 

■fo of a rotation is 36°, or 2 h 24" ; and so on. We must 
remember, when we use the names of divi time to 

denote angles, not to allow ourselves to be puzzled by their 
usual meanings. A fraction of a rotation is one thing, and 



214 Outlines of Astronomy. [Sec. 406. 

a fraction of the time occupied by the rotation is another. 
A wheel may go round ten times in what we usually call a 
second of time, and yet each of its rotations contains 24 
hours, and therefore 86.400 seconds of time, understood in 
the sense of angles. Our measurements of time are made 
by means of the rotation of the Earth with respect to other 
objects, as was shown in the last chapter ; but we shall 
that when astronomers use the word hour as meaning 
rotation, this angle generally answers to the division ot time 
called a sidereal hour, and not to an hour of mean time. If 
we were now to decide for the first time how a rotation should 
be divided, we should probably take some simpler method of 
doing it than any of those just described ; but we must be 
content, for the present at all events, to follow the long estab- 
lished custom of mathematicians. 

407. We sometimes reckon in decimal fractions of a de- 
gree, an hour, or a minute of arc or time, instead of redu 
the fractions to a lower denomination. Thus 3^.8 1 , or 3 b 
48 nQ .6o, is the same as } h 48" 36*. It may also 1 

by 57°- " 5< OI by 57° 9'- 

408. In rectilinear movement, all the points of the moving 
object go equally fast (395) ; but in rotation, some points do 
not move, and the others move slower the nearer they are to 
these (33). In rectilinear movement, all the straight Bud 
the moving object keep their directions unchanged, and all 
its planes keep their positions (40 1) J while in rotation, no 
plane not perpendicular to the axis keeps its position, and 
no line, except the axis and the lines parallel to it, keeps 
its direction. We know nothing, of course, of any actual 
rotations, or rectilinear movements ; these are only the names 
of movements which we find it convenient to consider 
composing some of the actual movements about us (1 14*. 

409. Suppose one of the points of a rotating body to be 
moving at the same rate with each of the points of a body 
having rectilinear movement. When a whole rotation has 
been completed, this point will have described a line which, if 
it were straightened out, would be equal to the distance trav- 



Sec. 409.] Geometrical Terms. 215 

ersed during this rotation by the body having rectilinear 
movement. If the line is not straightened out, or rectified, 
the usual expression, it will form a ring round 
the axis. A ring of this kind is called the circumference 
of a circle. Very often, indeed, it is itself called a circle, 
for the sake of shortness ; but a circle is properly that part 
of a plane inclosed by its circumference. We have seen that 
a circle is an ellipse without any eccentricity (145), or with 
both its foci at its centre. When a circle is described by 
means of a rotation, its centre is of course the point in the 
- nearest to its circumference. For instance, if a hori- 
zontal circle is drawn by means cf a pencil fastened to a 
thread tied to an upright pin, the pin will represent an axis 
of rotation, and the place where it pierces the paper is the 
centre of the circle. A diameter of a circle is any straight 
line passing through the centre and ending in the circum- 
ference on each side : and a radius is half a diameter. 

410. The circumference of a circle may be considered in 
two ways ; either as a line, having a certain length when 
regarded as rectified, or as a mere sign of the rotation by 
means of which it maybe considered to have been described. 
In the first case, it may be measured in inches, or in any 
other measure of length ; in the second case, it is divided, 
like a rotation, into equal parts called arcs, each arc answer- 
ing to an angle and being called by the same name with that 
angle. Thus, an arc of 90 , or 6\ is a quarter of the whole 
circumference of any circle, no matter how large the circle 
may be. 

411. When the circumference of a circle is regarded as a 
line of a certain length, its length may be compared with that 
of any one of its diameters, which are all equally long. It 
has been found that every circumference is a little more than 
three times as long as its diameter ; but the length of the diam- 
eter is not contained in that of the circumference any number 
of times which can be stated in figures. For want of under- 

dinc: that this is a known fact, many people have wasted 
their time in trying to square the circle, as it is called. The 



216 Outlines of Astronomy. [Sec. 41 r. 

ratio between the circumference and the diameter of any 
circle is commonly denoted by the Greek letter 77, the name 
of which is Pi. The value of tz is very nearly \\§ ; that is, 
if any diameter is divided into 113 equal parts, there will he 
almost exactly 355 parts of the same length in the circum- 
ference. The figures in these numbers are easily remem- 
bered, from the order in which they come ; 113,355. The 
letter 7r has other uses in astronomical computations besides 
that just explained ; in particular, it often stands for certain 
angles of parallax (357). 

412. If a circle rotates about one of its diameters as an 
axis, it describes a sphere (76, 159). the centre of which is 
the same with the centre of the circle. If a sphere is cut 
in two by a plane, the boundary between the two parts into 
which the surface of the sphere is thus divided must be the 
circumference of a circle. When one surface is cut bv an- 
other, the boundary thus formed is called an intersection. 
The intersections of planes with the surfaces of spheres are 
generally called circles, although they are properly circun 
ences. When a plane passes through the centre of a sphere, 
its intersection with the sphere is a great circle. When a 
sphere is formed by the rotation of a circle, the diameter of 
that circle perpendicular (402) to the axis describe- 

circle of the sphere. The ends of the diameter which se- 
as an axis are the poles of this great circle, and of all the 
small circles which lie in planes parallel to its plane. 

413. Hence, if we draw a diameter through any sphere, its 
ends are the poles of the great circle and of all the small cir- 
cles the planes of which are perpendicular to this diameter. 

414. If two straight lines cross each other, and one of 
them is the axis of a rotation bv which the other is carried 
round it, the moving line will describe a surface called the 
surface of a double cone. If a double cone is cut by a 
plane, the intersection of the two fs a circle, an ellipse, a 
parabola, or a hyperbola (228). according to the position of 
the plane. All these figures are called conic sections. 
The parabola may be reduced to a straight line, the hyperbola 



Sec. 414-] Geometrical Terms. 217 

to two straight linos, and the circle or ellipse to a point, 
when the plane which forms the intersection cuts the cone 
into two or four parts exactly like each other. 

41;. If a rotating straight line is perpendicular to the axis 
ration, it describes a plane to which the axis of its 
rotation is perpendicular (403). instead of a double cone. In 
this case, after a rotation of 90 , the rotating line is perpen- 
dicular to any line which at first coincided with it, and it is 
n perpendicular to it after a rotation of 270 . 

What is called the angle between f wo planes is the 
amount o( rotation about their intersection (412) as an axis 
which would bring one ot them to coincidence with the other. 
If this angle is 90 , the planes are perpendicular to each other ; 
and in this case the rotation may take place either way through 
90 before the planes coincide. This may be illustrated by 
holding one leaf of a book vertical while the leaves on each 
side of it are horizontal (252. 255). But if the angle is not 
90 , then the rotating plane will have less rotation to make 
one way than the other in order to come to coincidence with* 
the stationary plane. In such cases the smaller angle of the 
two is usually considered as the angle between the planes. 

417. The angle between two straight lines which cross 
each other is the amount of rotation which one of them would 
have to make, about an axis perpendicular to both of them, in 
order to come into coincidence with the other. This angle is 
the same with that between two planes, each of which con- 
tains one of the lines, and both of which are perpendicular 
to the plane which contains both of the lines. This may be 
illustrated by folding a piece of paper once, and setting it on 
a table so that the create is vertical The angle between the 
two lines drawn where the paper on each side of the crease 
>n the taLle (supposing these lines to be straight), is 
, with that between the two parts of the paper ; and 
the line of the crease is the axis about which the rotation 
which measures the angle is to be made. The crease, of 
course, must be made perpendicular to the lower edge of the 
paper. 



218 Outlines of Astronomy. [Sec. 418. 

418. A plane polygon is a part of a plane enclosed by 
straight lines ; and a spherical polygon is a part of the sur- 
face of a sphere enclosed by arcs of great circles. These 
lines or arcs are the sides of the polygon ; the angles of the 
spherical polygon are the angles between the planes of the 
great circles which form it, and those of the plane polyg 
are the angles between its sides (or between planes contain- 
ing its sides and perpendicular to the plane of the polygon). 
In spherical polygons, the sides are not considered as dis- 
tances, but as angles (410). 

419. A triangle is a polygon with three sides and hence 
three angles. The angles of a plane triangle, taken together, 
always make just 1S0 ; the angl< Spherical triangle, 
taken together, always make more than 180 . The sides and 
angles of a triangle are called its parts. 

420. An angle of 90 is commonly called a right angle ; and 
a right triangle is one which has a right angle for one of its 
angles. 

421. Every polygon may be divided into triangles; and 
some of the parts of any triangle may be found by Calcula- 
tion if the others are known. Usually, it is enough to know 
three parts of a triangle to determine the other three. 

422. Every line which is not straight may be regarded 
as having a particular direction at any one of its points. 
A straight line touching it at any point and having the same 
direction with it at that point, is tangent to it at that point. 
The point where the tangent touches the other line is called 
the point of contact. A line drawn through the point of 
contact and perpendicular to the tangent is normal to the 
other line. 

423. In like manner, a plane may have a point of contact 
with some surface which is not a plane, but which is con- 
sidered as having the same position (401) with the plane at 
the point of contact ; the plane will then be tangent, and a 
line perpendicular to it will be normal, to the other surface at 
the point of contact. 

424. Thus, if the top of a table is smooth and level, a per- 



Sec. 424.] Geometrical Terms. 219 

fectly smooth rounded stone lying on the table may be con- 
sidered as having, at its lowest point, the same position as 
the upper surface of the table ; and a vertical line through 
this point of contact between the stone and the table will be 
normal to the under surface of the stone as well as perpen- 
dicular to the upper surface of the table. If the stone is 
considered as divided by a vertical plane passing through 
its point of contact with the table, this normal line will like- 
wise be normal to the intersection of the plane with the under 
surface of the stone, and perpendicular to the intersection of 
the plane with die upper surface of the table. 



220 Outlines of Astronomy. [Sec. 425. 



CHAPTER IX. 

O P T I C A L T E R M S. 

425. What we call light is a movement of some kind, as 
yet little understood; but it has been found possible to lay 
down a number of rules about light which will hold good 
whatever may be learned about it hereafter. 

426. Any line along which light travels is called a ray of 
light What we commonly call a ray. or beam, of light, con- 
tains as many of these geometrical rays as we please. R 

Of light Continue Straight as Inn- as the matter through which 
the light is passing continues to be of the same kind, 
kind of matter through which light is passing may be called 
a medium of light; but two media are different even if 
the matter which composes one differs only in density from 
the matter of the other, and is like it in every other res; 
A ray of light is said to be incident upon any surface on which 
the light shines. 

427. Any object through which light cannot pass is called 
opaque. The light which comes to an opaque object mav be 
absorbed by it (51) or reflected by it ; generally it is partly 
absorbed and partly reflected. When most of it is absorbed, 
the object looks black : and the colors of opaque objects are 
due to the kinds of light which they reflect, some of them re- 
flecting rod light, some blue, and so on. Ordinary light may 
be separated into light of diffeient colors in other ways than 
by absorption and reflection, as we shall see. 

42S. When any light is reflected, the angles of incidence 
and reflection are equal : that is, if a ray of light is normal 
(423) to the reflecting surface at the point where it strikes 
that surface, the light comes back as it went ; or, in other 
words, the reflected ray coincides with the incident ray: and 
in any case, if we draw a line normal to the surface at the point 



Sec. 428.] Optical Terms. 221 

where the ray touches it, the reflected ray lies in the same 
plane with the incident ray and the normal line, and the inci- 
dent and reflected rays make equal angles with the normal 
line. Hence, from all but very smooth surfaces, reflected 
light is thrown about in a variety of directions, so that any 
particular beam of light is broken up. Reflection of this kind 
i> called irregular. But if a surface is very smooth, and a 

Jit beam of light falls upon it from any particular direction, 
: ly all that part of the beam which is reflected at all may 
be reflected in some other particular direction. The reflecting 
surface, if seen from this last direction, will then seem to shine, 
but not to have any particular color. This sort of reflection is 
called regular. 

429. Objects through which some light can pass are called 
transparent The surface common (392) to two transparent 
media (420; is called a refracting surface. When light comes 
to a refracting surface, some of it is usually absorbed, some 
reflected, and some refracted. A ray of light is said to be 
refracted when its direction is changed by its passage 
through a refracting surface. The amount of the refraction 
of any ray of light at any refracting surface is the angle by 
which the direction it actually takes after passing that surface 
differs from the direction it previously had. This angle de- 
pends on the properties of the two media to which the refract- 
ing surface is common, and particularly on their density as 
compared with each other (426). Suppose that at the point 
where a ray of light passes through a refracting surface a line 
rawn normal to that surface. If the ray coincides with 
the normal line before reaching the surface, this coincidence 
will continue beyond the surface, and the ray will not be re- 
If the incident ray is not coincident with the normal 
line, the direction of the refracted ray which has passed the 
surface will differ from that of the normal either more or less 
than before. If more, the medium from which the light comes 

- lid to have more refractive power than that which the 
light enters ; if less, the medium which the light enters has 
more refractive power than the other. For example, when a 



222 Outlines of Astronomy. [Sec. 429. 

slanting ray of light enters smooth and level water, the re- 
fracted ray is more nearly vertical than the incident r 
when a slanting ray of light comes from the water to the air, 
the refracted ray is less nearly vertical than the incident 
ray. Hence water is said to have more refractive power 
than air. As a general rule, if one object is denser than 
another, it has also more refractive power than that other 
object. 

430. It may happen that a ray, on coming to a refracting 
surface beyond which lies a medium of less retractive power 
than the medium through which the light has been passing 
is required by the laws of refraction to change its direction 
so much as not to pass through the surface at all. In this 
case, the surface becomes, for that particular ray. the surface 
of an opaque body, and the ray is reflected* This effect is 
called total reflection, and opticians often take advan* 

of it to make a glass prism serve instead of an Opaque 
mirror. 

431. A prism, property speaking, is any geometrical solid 
described by a plane polygon having rectilinear motion. If 
the polygon is a triangle, the prism is triangular ; and the 
glass prisms used for optical purposes are generally of this 
kind. If the triangle describing a triangular prism has one 
right angle, the prism is called a rectangular prism. A rec- 
tangular glass prism, if it is to be used as a mirror, is gener- 
ally made so that the triangle by which it may be supposed 
to be described has the sides which form its right angle 
equal to each other. Now if a ray of light is supposed to 
enter the prism perpendicular to one of these sides, it will 
not be refracted (429), but will keep on in the same direction 
as before, to the side of the prism opposite to its right ang 

It cannot pass through this side ; for if it passed into the air 
at all, it would be more nearly perpendicular to the surface 
through which it had just passed than is consistent with 
the refractive power of glass as compared with that of air. 
Hence it is reflected ; and as the reflecting surface is equally 
inclined to the other two faces of the prism, the ray lea 



Sec. 431] Optical Tkrms. 223 

the prism by its third side, to which the course oC the light 
3 now been made perpendicular; so that, as before, no 
curs. A good prism, used in this manner, re- 
- more light than the best opaque mirror. 

When a glass prism is used, not to reflect light, but 
to refract it, the side of the prism through which the light 
enters is not set perpendicular to the direction from which 
the light comes, so that the light is refracted once on enter- 
ing the prism ; and the prism is usually made of such a 
shape that the light may be refracted again as it comes out 
of the prism into the air. Different kinds of light diller in 
ingibility ; that is, when several kinds of light come to a 
refracting surface, one kind is more refracted than another. 
An incandescent object often gives out light of a great many 
kinds mixed together; every solid or liquid object does this 
when it is made incandescent. One use of prisms is to 
rate different kinds of light from each other by means 
of their different refrangibilities. One of the kinds of light 
which come to a prism in some particular direction may be 
made (by total reflections within the prism, or otherwise) to 
. after coming out of the prism, in this same direc- 
tion ; while each of the other kinds comes out in some other 
direction of its own, not very different, but still distinct, from 
that in which it entered the prism. But this depends on the 
shape of the prism, and on the direction in which the light 
comes to it. A flat piece of glass, with two plane faces paral- 
lel to each other, like a well-made window-pane, is one kind 
of prism. The light which passes through it is refracted at 
each face of the glass ; but the second refraction restores 
h kind of light to the direction it had before the first re- 
so that the different kinds of light are not turned 
rent directions by their passage through the glass. 
In fact, as every one kn<> Ordinary window-pane has 

no very noticeable effect of any kind on the appearance of 
through it ; and we need I ider 

the small effects which it may be shown to prodv 

433. A beam of light is said to be dispersed when the 



224 Outlines of Astronomy. 433. 

directions of the various kinds of light composing it are 
unequally changed. When dispersion is occasioned by re- 
fraction, its amount is partly dependent on the nature of the 
refracting medium. For example, one kind of .lied 

crown glass, has less dispersive power than another kind 
called flint glass. Hence, if different kinds of light o 
all in the same direction to a surface of flint glass, and j 
through it, their directions in the glass will be more unlike 
each other than they would have been if the glass had been 
crown glass. By taking advantage of this fact, we can put 
pieces of different kinds of glass together so that they will 
refract one of the kinds of light coming to them in any par- 
ticular direction about as much as tin I another: 
so that one kind of the light which comes to them in some 
particular direction will leave them in about the same direc- 
tion, while they change, more Of less, the directions of the 
other kinds of this light : hat the light may be both 

refracted, as in the first case, and 1 - in the 

second. 
434. It appears from the account just given of refl< 

and refraction, that any very smooth reflecting or refracting 
surface may be sending out a great deal of light in some 
particular directions, but in no others, so that it looks bright 
from one place and not from anoth 
smooth, that of ordinary wood, met d. or cloth, for : 
may be considered as sending out in all dir 
the light which comes to it ; and the surface of a body which 
gives out light o( its own also sends out this light in all 
directions. When light is sent out in all directions from 
particular point, some of it may be stopped at once by the 
very body to which this point belongs : and oth of it 

maybe absorbed, reflected, or refracted by the bodies they 
meet after having travelled to a greater or less distance. 
That part of the light sent out from any particular point, and 
coming straight to any particular surface which we may be 
considering, is called a divergent pencil of rays incident 
upon the surface from the point. Every pencil of this kind, 



Sec. 434.] Optical Terms. 225 

then, is considered as beginning at some point and gradually 
it until, when it reaches some surface, it is lai 
to cover it exactly. Other pencils of rays may of 
course be incident at the same time on the same surface. All 
these pencils coincide at this surface, and separate from each 
other more and more as we follow their courses backward to 
tints from which they start. 
435. Now suppose the surface on which a divergent pencil 
is incident to be the pupil of a man's eye, and the point 
from which the pencil starts to be on the surface of a hill ten 
ay. It is clear that if straight lines are drawn from 
this point to opposite sides of the pupil which receives the 
light, these lines will be nearly parallel ; for in the course of 
ten miles they have separated from each other only about 
one-tenth of an inch. So, too, if a divergent pencil of light 
:s from a point in the Moon and is incident on the roof 
of a large building, the rays of this pencil which diverge most 
from each other are still very nearly parallel. The largest 
momical instruments are only a few feet across : so that 
- obvious that all pencils of light coming to these instru- 
ments from points in the celestial objects which are observed 
through them may be considered as made up of rays of light 
parallel to each other. A pencil, the rays of which are con- 
red to be parallel to each other, is called a parallel 
pencil. 

By means of properly shaped reflecting or refracting 
surfaces the directions of the rays of any pencil may be 
changed with respect to each other. The instruments made 
with reflecting surfaces, suited to this purpose, are called 
mirrors or specula ; those with refracting surfaces are 
<>f the kind called lenses. The surface of a mirror 
may be either plane, convex, or concave. A rounded sur; 

on which a plane must lie in order to 

e a point of contact with it (423). and conca/3 on the 

oth- The surface of a - one kind of convex 

surface, and that of the air which it is one kind of 

have both *ite sun 

•5 



226 Outlines of Astronomy. [Sec. 436. 

convex, both concave, one convex and the other concave, or 
one plane and the other convex or concave. If both were 
plane, it would be a prism rather than a lens. It' one is con- 
vex and the other concave, the lens may be considered on 
the whole convex if the convex surface is the more rounded 
of the two, and concave, if the concave surface is the more 
rounded. 

437. A concave mirror, or a convex lens, makes the rays 
of any pencil of light incident upon it less divergent than 
they were before. It may make them parallel, or even con- 
vergent, so that they come together more or less exactly at 
some point in their new course. Beyond this point the pencil 
is again divergent ; but it usually forms the whole of the light 
diverging from that point, while it was only part of the 
light diverging from the point where it began (434). 

438. A convex mirror, or a concave lens, makes the rays 
of any pencil of light incident upon it more divergent than 
they were before. It may turn a convergent pencil into a 
parallel or into a divergent pencil. 

439- l*y putting together two lenses made of different sorts 
of glass, we can obtain a lens which will act in either of the 
ways just described without noticeably dispersing the difl 
ent kinds of light which we may regard ling the lens 

in the direction of any particular ray (433). A lens of this 
kind is called an achromatic lens. 

440. The chief difficulty in explaining the facts of optics 
is that pencils and rays of light are apt to be mistaken for 
each other. To avoid this difficulty as much as possible, we 
will hereafter take little notice of rays, and consider only the 
course of pencils of light. To show how an image of an 
object may be formed by means of the pencils of light coming 
from different parts of that object, we have only to shut out 
from some room or small building all light what ept 

what comes through a small hole left in one side of the room, 
and facing towards some object — a tree, for example — which 
is seen against bright sky or clouds. An image of the tree 
will be thrown upon any thing in the room which may be 



Sec. 440.] Optical Terms. 227 

opposite the hole ; a white screen of some kind will answer 

; to receive the image. In this case the light by which 

ge comes from behind the tree, and the image 

If is a kind of shadow. Still, as the tree really reflects 

e light towards the hole, although still more light comes 

a behind the tree, we may speak of pencils of light coming 

from the tree to the hole. The pencil which starts from the 

tip of one of the tree's branches, and passes through the hole, 

makes a little spot of dim light upon the screen. This little 

spot forms the image of the tip of the branch, and looks dark 

upon the screen because there is brighter light around it 

coming from behind the tree. The image of every point on the 

surface of the branch turned towards the hole is likewise a 

little spot of dim light on the screen. These spots overlap 

each other, more or less, according to the size of the hole ; 

so that if the hole is too large, no image can be seen. But 

if the hole is small enough, the image of any particular point 

in the branch will not cover up the images of any other points 

except those close to it. Accordingly, the shape of the branch 

will be traced out, though not very clearly, upon the screen. 

During eclipses of the Sun, the openings among the leaves 

of trees may occasion the appearance of little sickle-shaped 

images upon the ground beneath them. This effect depends 

on the principles just stated. 

441. The images upon the screen will be inverted; that 
is, the pencils coming from any two points outside of the 
hole must cross each other at the hole, so that if one of 
the points is above the other, its image must be below that 
of the other ; and if one is east of the other, its image must 

of that of the other. Hence the picture on the screen 
le down, and its sides stand the contrary way from 
t which the image represents. 

442. If we wish to make the image plainer and yet keep it 

we must make the hole larger, so that 
more light may come in. and fill it up with a convex (456) 
lens; a lens which is also achromatic II, of com 

be best. This lens must have enough refractive power to 



228 Outlines of Astronomy. [Sec. 442. 

make the rays of each pencil come together in a single point 
somewhere within the room. If the pencils all start from 
points about equally far from the lens, the points where the 
rays of each of them all meet again will be about equally 
from the lens ; for instance, if any pencil starts from a point 
two hundred feet from the lens, and its rays all meet again 
inside tiie room and ten feet from the lens, the rays of any 
pencil incident upon the lens from another point about 
hundred feet away from it will also meet again inside the 
room and about ten feet from the lens. The lens, if it is a 
good one, will not greatly alter the general course of each 
pencil ; it will only alter the shape of the pencil, making it 
convergent, instead of divergent, as before (437). 

443. If the screen is held close to the lens, the image will 
be confused, becau.se each pencil will make a large spot on 
the screen, and these spots will overlap each other ; but if the 
screen is then gradually moved away from the lens, the S] 
will grow smaller and smaller, while the image -rows more 
and more distinct. When the screen is held so far from the 
lens that each spot may be extremely small, the image will 
be much more distinct than it would be without the l< 
even if the hole were so small that only just enough light 
could come in to make the image appear at all. If the screen 
is moved still farther away from the lens, the pencils will 
again widen out and the image will become confused. 

444. A dark box, into which light is admitted through a 
convex lens, so that images may be formed on a screen 
inside, is called a camera obscura, or very often simply a 
camera. Instruments of this kind are used in making pho- 
tographic pictures. But for various reasons, it is difficult to 
make a camera which will represent an extensive view ( 
rectly. The shapes of objects, especially of those towards 
the border of the picture, are apt to be altered even in the 
best cameras. To correct as far as may be this change of 
shape, which is called distortion, several lenses are generally 
used instead of one. 

445. Any point where the rays of a pencil of light are 



445-] Optical Terms. 229 

•e to meet by means of a lens or mirror is called a focus. 

name o( focus is also given to any point from which a 

pencil starts, or is made to seem to start. A concave lens, 

. which makes a pencil more divergent than it 

4.38), makes the pencil seem to start from a point 

- than that from which it really starts ; and 

irent starting-point of the pencil is often called a focus. 

What is usually meant by the focal length of a lens or 

mirror, is the distance from it at which would be found 

the focus given by the lens or mirror to*a parallel pencil of 

: incident upon it (435) - 

44-. The eye of an animal consists in part of an apparatus 

like a camera obscura. The screen on which the images 

of objects are formed within the eye is called the retina. 

Images formed on the retina are of course inverted (441). 

question is sometimes asked why we do not see objects 

!e down, as their images are placed on the retina. But 

8 question is rather absurd, for no eye sees its own retina, 

or can tell any thing about the shape and place of an image 

led upon it. We see objects outside of us by means of 

their images ; we do not see the images themselves. How 

it is that we see any thing at all has not yet been fully 

found out. 

There is a spot in the retina on which an image may 

be formed without making the eye see the object by which 

that image is formed. Since we commonly use both eyes in 

looking at any object, we see it with one eye or the other, 

r we stand with respect to it. But if one eye only is 

used, an object which is in sight when it is either directly in 

or far towards its outer side, may be out of 

tin direction from the eve. between 

the * s just mentioned. For instance, when a ship 

•r at a considerable (1; : he 

rand keeps the other eye still, the ship will | 
out of his sight, and come into sight again when its in, 

the spot on the retin e formed 

out making the ship visible. 



230 Outlines of Astronomy. [Sec. 449. 

449. The distance which we suppose ourselves to see 
between any two points is merely an angle. Suppose a 
straight line to be drawn from each point to its image on the 
retina. If these two lines do not cross, they must at all 
events pass close by each other somewhere in the eye. Now 
the angle between the direction of one line and that of the 
other, or, in other words, the angle between one line and a 
line drawn across it parallel to the other (417), is all that 
we can know, by the mere sense of sight, about the distance 
between the two points from which the lines are drawn. 

450. If these points are near enough to the observer to 
make a noticeable difference between their directions from 
one of his eves and from the other, he can then make an 1 
mate of their actual distance from him even without mo> 
his head ; and if he moves a little, he sees them in so many 
different directions that it is easy for him to judge pretty 
rectly how far away they are. When he knows this, he 
tell how far apart they are by means of the angle between the 
lines drawn from them to either of his eyes. All tl, 
dilations are made without the need of any distinct thought 
at all ; in a rough way, it is true, but still corre< tly enough 
for the ordinary wants of life. Calculations of a like kind, 
made accurately from the angles found by exact observation 
with instruments, give us the means of rinding the distance 
from us, and the distance apart, of objects far from the places 
where the observations are taken. 

451. Most people are in the habit of thinking that they 
see actual distances ; but the fact is that their knowledge of 
these distances, so far as it is got by means of sight, depends 
on observations of parallax (357), and on rough calculations 
made from these observations, so quickly and easily that 
neither the observations nor the calculations are noticed, and 
the distances measured by means of them are thought to 
have been seen. Before people can learn to draw, they have 
to break themselves of the habit of overlooking what they 
really see (267). 

452. The angle between the straight lines drawn from any 



SEC. 45 2 ] Optical Terms. 251 

two points to a third is called either the visual angle or the 
angular distance between the first two points seen from the 
third. is pro; it all. Distances 

are amounts of rectilinear motion, and angles are amounts oi 
as it is also 1 tngular motion. However, 

the phrase angular distance may sometimes be a convenient 
one to u 

When the thickness of a pencil of light is small com- 
pared with its length, we may speak of the direction of the 
pencil without any great want of exactness, even if it is not a 
parallel pencil ; for none of the straight lines drawn from one 
end of it to the other can differ much in direction. Accord* 
/\\ we may say that the angular distance between two 
points seen by any observer is the angle between the pen- 
cils of light which reach his eye from those points. 

454. The angular diameter, or, as it is often called, the 
apparent diameter, of a celestial object, is the angular dis- 
tance between the ends of any one of its diameters which is 
drawn perpendicular to the direction of the object from the 
observer. That is, this apparent diameter is the angular dis- 
tance between any two opposite points on the limb of the disk 
of the object observed. 

In order to see any object distinctly, the eye must 
bring each pencil of light which comes to it from that object 
irly to a focus (445) upon some part of the retina. If a 
pencil of light is strongly divergent when it enters the eye, it 
reaches the retina before it has been brought to a focus. Hence 
an object held less than about three inches from an ordinary 
eye cannot be seen distinctly. Ordinary eyes can adapt 
1 pencils which are either parallel or only slightly 
divergent. n adapt themselves only to 

sisted by « <>n- 
that the pencils wl ich them ma] 

rgent than they would be except for the 

45 r »- If a convergent pencil of light enters an ordinar. 
it is brouglr. . i which it becomes a divergent 



232 Outlines of Astronomy. [Sec. 456. 

pencil, before reaching the retina. Hence, if an object is 
looked at through a convex lens of such power that it turns 
the divergent pencils reaching it from the object into conver- 
gent pencils, the object ordinarily looks indistinct. But far- 
sighted eyes can adapt themselves to slightly convergent 
pencils of light, and not to divergent pencils ; so that they 
have sometimes to be assisted by convex lenses. They can 
usually see distant objects without assistance, because a 
pencil of light reaching the eye from a point far away may 
be considered as a parallel pencil. 

457. If a point is sending out light in all directions, then, 
at any particular distance from this point, its light must be 
Spread OUt over the surface of a sphere enclosing the point at 
that distance. Now, as is shown in works on geometry, the 
surfaces of spheres are to each other as the squares of their 
diameters, or as the squares of their radii. That is, if the 
diameter of one sphere is twice that of another, it will have 
four times as much surface ; if the diameter of the - 
sphere is five times as long, its surface will be twenty-five 
times as great, as that of the second sphere. Hence the 
brightness of a Single point will generally lessen in proportion 
to the increase of the square of its distance from the eye. But 
the visual angle between any two points of an object looked 
at will also diminish at the same rate. Hence an object d 
not necessarily look fainter at a distance than close at hand ; 
for the closer packing of its points in the image of it formed 
on the retina will make up for the greater dimness of each 
point when seen from a distance. But much of the light of a 
distant object may be absorbed on its way to the eye, and 
this is the reason why distant terrestrial objects look fainter 
than others of really equal brightness which are close at 
hand. 

458. Celestial objects, however, do not become dimmer in 
proportion to their distance. From any place just outside 
the Earth's atmosphere, the Moon would probably look as 
bright, though not as large, as it would from a place within 
ten thousand miles of it ; for although it is possible that some 



Sec. 458.] Optical Terms. 233 

light is absorbed in passing through the ether, or whatever 

fill the spaces between the various celestial objects, this 

irption is evidently small. If it were large, the Moon 

would look decidedly brighter in perigee than in apogee (177, 

190' 

459. The stereoscopic effects, as they are called, which 

depend on our ordinary use of two eyes at the same time, 
have so little to do with astronomical observations that they 
need not be described here. 



234 Outlines of Astronomy. [Sec. 460. 



CHAPTER X. 

Til E TELESCOPE. 

460. Most people have occasionally looked through convex 
lenses, and are aware that such lenses usually magnify the 
objects seen through them. That is, a convex lens usually 
increases the angular distance between any two points in an 
object looked at through the lens. The reason for this is as 
follows : — 



If we suppose the eye to be placed at E, in the i 
above, the visual angle (452) between two points, one at 13 
and the other at C, will be the angle BEC, formed at E by 
the lines BE and CE. Now suppose a convex lens to be 
placed between the eye and the object to which the points B 
and C belong. The effect of this lens will be to make the 
pencil of light reaching it from B less divergent than it was 
before passing the lens. The same effect would have 1 
produced without the lens if the point B had been moved 
farther away, to some such point as M in the figure. So, too. 
the effect of the lens upon the pencil reaching it from C might 
be produced without the lens if C were removed to some such 
point as N in the figure. The proper places for these points 
M and N may be determined by calculations for which there 
is no room in this work. They depend on the exact shape ot 
the lens, the material on which it is made, and its place with 
respect to the points B and C. But M, N, B, and C, will all 



Sec. 460.] The Telescope. 235 

lie nearly if not exactly in one plane ; and we will suppose 
m to lie exactly in one plane. Then, if we draw lines from 
through 13 and from N through C, these lines must cross 
each other at some such point as L in the figure. This point 
L will be in fact somewhere near the middle of the lens ; and 
it is called the optical centre of the lens. 

Now if the eye were at L. the visual angle between B 
and C would be BLC ; and this visual angle would remain 
unchanged by the removal of the points B and C to M and N. 
But as tl a at E, there may be a difference between the 

lal angle BEC of the points B and C and the visual angle 
MEN ot the points M and N. In ordinary cases, such as 
that represented in the figure, the angle MEN is larger than 
the angle BEC. Hence the lens magnifies the distance be- 
tween the points B and C, and in like manner magnifies the 
distance between any two points in the object looked at 
through the lens ; so that the object looks larger than it 
did before the lens was placed between it and the eye. A 
convex lens used in this way does not invert the objects seen 
through it. In the figure, for example, M is above N just as 
B is above C. 

462. Now suppose that the lens is taken away and that the 

eye is brought from E to L. The visual angle between the 

points B and C is now BLC ; and this angle is not only 

*er than BEC, but larger even than MEN. This appears 

he dotted lines drawn from L parallel to ME and NE so 

> make an angle at L equal to the angle MEN. It seems, 

then, that an object seen through a convex lens looks no larger 

than it would look if the lens were taken away and the eye 

brought a little nearer to the object. We notice the magnify- 

e fleet of a lens because we are not used to having lenses 

constantly placed between us and other objects and taken 

away again ; but we are so used to moving a little one way 

or the other that we do not notice how much larger an object 

looks when it is a few inches from our eyes than when it is a 

(207). 

<nvex lens, however, becomes of real serviu 



236 Outlines of Astronomy. [Sec. 463. 

magnifier when the eye has already been brought as near the 
object to be observed as it can be brought without making 
the object indistinct (455). Writers on optics sometimes 
speak as if the eye were always brought as close as possible 
to the object observed. They say, accordingly, that a com 
lens magnifies only because it enables the eye to be placed 
closer to the object than it could otherwise be placed. But 
this is a careless statement ; and every one who has amused 
himself with a magnifying-glass knows that without chang 
the distance of his eye from the letters of a book he can n 
nify them by means of the lens. 

464. A concave mirror magnifies objects held near it for 
much the same reasons as those which account for the like 
effect of a convex lens. But this use of concave mirrors 
is not required in the construction of astronomical instru- 
ments. 

465. For astronomical purposes, we need instruments 
which will magnify distant objects. Now every pencil of 
light which reaches our instruments from a distant ol 

is practically a parallel pencil (435). If. then, we view a 
distant object through a convex lens held near our e 
we shall merely make our view of the object indistinct ; 
for each parallel pencil of light from the object will become 
a convergent pencil after passing the lens (437, 456). Hut 
supjxxse that the focal length of the lens (440) is less than 
its distance from the eye. Every pencil of light which then 
reaches the eye from any distant object seen through the lens 
will be a divergent pencil starting from the focus to which 
the lens brought it before it reached the eye. 




c 

466. Suppose that the pencil of light from the point B is 
made by a lens to converge to the point M, while the pencil 
incident on the same lens from the point C converges to N. 
If we draw the lines MB, NC, their point of intersection, or at 



466.] The Telescope. 237 

all events the place where they come nearest to each other, 

not he tar from the middle of the lens. We will call 

point L. as before. After passing the focus M, the light 

.\ ill form a divergent pencil starting from M, 

not in all directions, but only along the continuation of those 

lines by which it came from the lens to M (437). If any 

pan this rgent pencil enters an eye placed at E, it will 

1 have come, not from B. but from M. In like man- 

. any light reaching the eye through the lens from the 

point C will seem to have come from N. It must be remem- 

ed that the lines in the figure do not represent rays of 

•. but are merely drawn to show the comparative size of 

tain angles. The direction of almost every ray must be 

Chang y its _'i a lens. 

The lines BM and CN cross each other at L, so that 
the image at M of the upper point B is below that at N of 
the lower point C. It appears, then, that objects will be seen 
inverted (441) when looked at through a lens which makes 
pencils of light from them convergent, and is held so far from 
the eye that before reaching it these pencils have passed their 
and have again become divergent. The difference be- 
tween this use of a lens and its use in a camera obscura is 
that when an image is formed on a screen, it is shown by 
irregular reflection (42S) from the screen, so that it may be 
seen by an eye placed anywhere within view of it: while if 
it is formed in the air it can only be seen when the eye is 
placed on that side of it towards which the pencils of light 
1 it proceed. 

The angle MLN is evidently equal to the angle BLC ; 
the proof of this equality may be found in geometrical text- 
book .ted. Hence the angle MLN may be con- 
the visuai etween the points B and C, 
ved from the point L; and if these points B and C are 
;>osed to be distant it will make little difference in 
the size of the visual angle between them whether we sup; 
tlu-m to be viewed from L or from K, since the distance 
bet. md the lens will be small compared with the 



238 Outlines of Astronomy. . 468. 

distance of either of them from the object looked at. Accord- 
ingly, we may say that MLN is equal to the visual angle 
between B and C, viewed without any lens. MEN is the 
visual angle between M and N ; and hence is the visual a 
between B and C viewed through the lens. J>Jow it" M and 
N are just half-way from L to E, the angles MLN and M 
will obviously be equal ; the proof of this equality is given in 
works 00 geometry. In the case just supposed, the lens will 
neither magnify nor diminish a distant object viewed through 
it. If M and N are less than half-way from L to E, the lens 
will diminish ; if more, it will magnify. It seems, then, that 
the eye must be placed close to the image of an object formed 
behind a convex lens, in order that the lens may make the 
object look larger. But if this is done, the view becomes in- 
distinct (455). This difficulty, however, can be got rid of by 

means of another lens, used in the manner already described 

(460), but in this case to magnify the image of an ol 
instead of the object itself. 

4^)0. An ordinary astronomical refracting telescope 
accordingly consists of two lenses, or rather of two com- 
binations of lenses, so that the various defects which the 
instrument would otherwise have may be collet ted as fai 
possible. One of these combinations of lenses is called the 
object-glass, and is used to form the image, which is then 
magnified by the other combination of lenses, called the i 
piece. The object-glass is usually made achromatic (4 
and the lenses of which it is composed are larger than tl 
of the eye-piece. The width of the object-glass is called the 
aperture of the telescope, and its focal length (440) is often 
called the focal length of the telescope. Every telescope 
usually provided with several eye-pieces of different magnify- 
ing powers. 

470, In the following figure, the telescope is supposed to 
reach from to L ; O being a point somewhere near the 
middle of the object-glass, and L a point somewhere n 
the middle of the eye-piece. The visual angle between I> and 
C as seen from E is of course BEC ; that between B and C 



47o.] The Telescope. 239 

seen from O is BOC. In the figure, BOC is decidedly 
2;er than BLC as is shown by the dotted lines within HOC, 




ich arc parallel to the dotted lines BE and CE, and there- 
fore make an angle with each other equal to the angle BEC. 
But the points looked at with a telescope are always much 
farther from it in proportion to its length than are the points 
B and C from O in proportion to the distance OL. In prac- 
tice, then, the angle answering to BOC is about the same as 
the visual angle between the points answering to B and C, 
looked at without a telescope. 

Let us suppose that the image of the point B is formed 
the object-glass at M, and that of the point C at N. The 
;le MON is equal to BOC (468), and therefore equal to 
the visual angle between B and C seen without the telescope. 
Now if the eve were at L, the visual angle between M and N 
would be MLN : and if the eye-piece is placed at such a dis- 
tance from M and X as to be most serviceable in magnifying 
the visual angle between them, the effect will be the same as 
if the eye were actually at L. The visual angle between B 
and C as seen through the telescope will accordingly be found 
rawing from E a line EP parallel to LM, and another 
line EO parallel to LN. The angle PEO is then equal to 
MLN, and therefore to the visual angle between B and C as 
1 the telescope, B appearing to lie somewhere 
along the line EP, and C somewhere along the line EO. 
472. An eye-pie* e, or any convex lens used in magnifying, 
■ effective when it is placed at a distance from the 
objr equal to its own focal length (44O. If tne 

the same as that of the obj 
M and N come half-' 
between the obj. ■. In t! the 

an- I and MLN would be equal (468), and the tele- 



240 Outlines of Astronomy. [Sec. 472. 

scope would neither magnify nor diminish. If the shapes of 
the object-glass and eye-piece are such that the focal length 
of the eye-piece is one quarter of that of the object-glass, the 
points M and N (provided that they are as near each other 
is always the case in a telescope) will be almost exactly four 
times as far from O as from L ; the angle MLN will then be 
very nearly tour times as great as the angle MON, and the 
telescope will be said to magnify four times. That is, the 
visual angle between any two points of a distant object will 
be made about four times as large as before by looking at the 
object through the telescope held in the usual way. If the 
object-glass is turned towards the eye, and the eye-] 
towards the object, the telescope will diminish the apparent 
width of the object to a quarter of what it seemed to be 
be tore. 

473. The general rule with respect to the magnifying 
power of any telescope is, that the telescope magnifies 
many times as the focal length of the eye-piece is contained 
in that of the object-glass. Hence no telescope can be said 
to have any particular magnifying power ; for all we have to 
do in order to change that power is to unscrew the eye-] 
and put in another. If the focal length of the new eye-pii 

is less than that of the old one, the magnifying power of the 
telescope is increased by the change ; if greater, it is dimin- 
ished. 

474. It appears by what has been said that the aperture 
of a telescope (469) has nothing directly to do with its magni- 
fying power ; for the focal length of a lens depends on its 
shape, and not on its size. Any particular eye-piece will 
magnify twice as much, when applied to a telescope the 
object-glass of which is so constructed as to have a focal 
length of twenty feet, as it will magnify when applied to a 
telescope the focal length of which is only ten feet ; although 
the object-glass of the first telescope may be two inches, and 
the object-glass of the second two feet across. But if an 
object-glass is very large, it is found best in practice to give 
it such a shape that its focal length will be considerable. An 



Sec. 474.] The Telescope. 241 

object-glass two foot across would in fact have a focal length 
bout thirty feet. In former times (before achromatic lenses 
e made), object-glasses which would now be considered 
.11 ones were made of great focal length when a high mag- 
nifying power was wanted ; but this made them inconvenient 
Modern opticians are not forced to get magnifying 
power by making object-glasses o\ great focal length. In- 
stead of this, they make eye-pieces of small focal length. 
The use of large object-glasses is not to magnify 
itly, but to admit a great deal of light. If the images 
formed by the object-glass of a telescope are not bright, they 
will look very dim when they are magnified by a powerful 
-piece. In this way a large object-glass may be said to 
increase the magnifying power of a telescope, since it allows 
1 use strong eye-pieces. However, the chief advantage 
1 large object-glass is that it helps us to see faint objects 
winch could not be seen at all with a small object-glass. In 
« such objects, eye-pieces which magnify little are 
preferred. Hence it often happens that the eye-piece actually 
used with a very large telescope is less powerful than one 
which may be used with a small telescope when bright objects 
are looked at : the Moon, for example, or a large planet. 

476. The Earth's atmosphere is one great hindrance to the 
use of high magnifying powers. All the disturbances in it 
p the transparency and the refracting power of its differ- 
ent parts in a continual state of change ; and the solid and 
liquid particles which float in it add to the effect of these 
disturbances. This effect increases with the increase of the 
unifying power applied by means of a telescope to any 
t. Hence it is seldom possible to use eye-pieces 
unifying more than five hundred times, even with the best 
and NoW in order to see the Moon as it 

. without a telescope, at a distance of forty miles 
(190). we must apply to it a magnifying power of six thou- 
sand; in oth- a power twelve times as great as any 
which the ordinal of the air will allow us to use with 
advanta r 

16 



242 Outlines of Astronomy. [Sec. 477. 

477. For the purposes of sight-seeing, a small telescope, 
with eye-pieces magnifying from fifty to two hundred times, 
is nearly as satisfactory as the largest telescopes that can be 
made. The use of great instruments is not to display won- 
derful sights in the sky, but to enable astronomers to see little 
things which are of importance in helping on the study of 
the construction of the universe. These little things are apt 
to be entirely overlooked by persons who have not learned 
to use telescopes for astronomical purposes, and even when 
they are seen are not thought interesting (388). In short, 
large telescopes are meant for work and not for show. 

478. A reflecting telescope differs from a refractor in 
forming images by means of a concave mirror instead of an 
object-glass. The light which this mirror reflects may be 
again reflected by other mirrors, so that the place of the 
image may be either behind the chief mirror (in which there 
must then be an opening for the passage of the light after its 
second reflection), or at one side of the tube of the teleso 

If no secondary mirror is used, the chief mirror may be 
a little slanting in the tube, so that the image is formed near 
one side of the mouth of the telescope. Whatever arrange- 
ment is adopted, the image is viewed, as in the refracting tel- 
escope, through an eye-piece placed near it, which maybe of 
any power thought to be advantageous. 

479. A reflecting telescope must be much larger than a 
refractor which gives equally bright and distinct images ; for 
more light is lost in the process of reflection than in that of 
refraction. The largest reflecting telescope hitherto built has 
a mirror six feet across ; while the aperture of the largest 
refractors is little more than a third as much. 

480. Spy-glasses and opera-glasses are seldom used as 
astronomical instruments, so that little need here be said of 
them. The spy-glass is an astronomical telescope with addi- 
tional lenses so placed that a second image is formed by the 
light proceeding from the first image. This second image is 
not inverted, so that when it is viewed through the eye-piece 
the object towards which the telescope is pointed is seen 



Sec. 4S0.] The Telescope. 243 

upright and not upside down. Some light is lost by this 

mgement, but glasses are meant to be used in 

magnifying objects scon by day under a strong light, this loss 
of light is unimportant In astronomical work, on the other 
hand, all the light that can be had is usually wanted, and the 
inversion of the object looked at is of no consequence. 

If the eye-piece of an astronomical telescope is set 
farther back from the image than usual, each pencil of light 
which comes out of it is convergent, so that nothing distinct 
can be seen by looking into the eye-piece in the usual way. 
But if a screen is held at a certain distance from the eye- 

e, a second image will appear upon the screen (50). If 
the screen is not used, this second image might be magnified 

1 second eye-piece placed beyond it ; and this arrange- 
ment of lenses is like that of an ordinary spy-glass. 

In the opera-glass, the eye-piece is a concave lens 
placed at a distance from the object-glass less than the focal 
: that glass. No image is formed, therefore, because 
each convergent pencil of light from the object-glass is turned 
into a parallel pencil by the eye-piece, before reaching the 
point where it would otherwise have come to a focus. But 
the direction of this parallel pencil is not usually the same as 
the direction which it had before reaching the object-glass 
and becoming convergent. Hence the angle between the 
direction of this pencil, and the direction of some other, may 
be increased by their passage through the lenses of the instru- 
ment ; and in this case the visual angle between the points 

1 which the pencils come is increased by these lenses, 
and the instrument magnifies. A telescope made in this way 

hortand easily handled ; and it does not invert the objects 

n through it. It is therefore convenient for many purposes, 
daily when mounted as it usually is, in the same frame 

- another like it, so that both eyes may be used at once. 
It has defect- r, which make it inferior for astronomi- 

cal use to the ordinal tor. For example, when we 

h to make measurements of any kind bj ofa tele- 

it sights of some I the instrument. 



244 Outlines of Astronomy. [Sec. 4 

This could not be done with an opera-glass, but may be 
done with an ordinary telescope, in the manner described 
below. 

483. If a mark of any kind, such as a metal ring, a fine 
wire, a spider's thread, or a line marked 01 
put into the tube of a telescope at the place where images of 
distant objects are formed by the object-glass, these images 
and the mark will be equally magnified by the eye-piece. By 
moving the telescope so that some point in the mark coin- 
cides with some point in an image, and afterwards bring 
the same point in the mark, by a second movement of the 
telescope, to coincidence with another point in the same 
image or a different one, we can measure the visual angle 
between the two points to which the mark has been brought 
For the angle through which the telescope was carried b) 
second movement can be measured in any one of a number 
of ways ; and the visual angle between the points is either 
the same as that through which the telescope was moved, or 
can be found from it by calculation. 

4«S4. Suppose, tor instance, that we wish to know the 
lar diameter (454) of the Moon. If we put a spider's tin 
across that part of the tube of a telescope where the in 
of any distant object will be formed, this thread will ap; 
when the telescope is pointed towards the Moon, as a black 
line crossing its disk. Now let the t< be moved so 

that the thread is a little beyond the Moon's preceding limb 
(1S3). If we now leave the telescope untouched, the Earth's 
rotation will move it. so that the thread will be carried acr 
the Moons disk from side to side. We can tell by calcula-. 
tion from the known movements of the Earth and Moon how 
much any terrestrial place moves with respect to the Moon 
in a given time. Hence if we note the time occupied by 
the thread in crossing the Moon's disk, we can calculate the 
apparent diameter of that disk as seen from the place of 
observation. 

485. All astronomical measurements are made by methods 
resembling this in principle ; we shall have occasion h< 



Sec. 485.] The Telescope. 245 

r to notice a few of these methods, but most of them are 

no interest except to practical astronomers. 

. The line of sight through a telescope may he vari- 
ously defined ; but in practice it is the straight line drawn 
from an)- point in a distant object to the image of that point 
formed by the object-- lass, when that image is formed at 

ie point chosen for the purpose, and marked by the sights 
put into that part of the tube of the telescope where the 
object-glass forms images. If the object-glass and these 

is move with respect to each other in the telescope, the 
line of sight is altered by the movement. Movements of 
this kind may be occasioned by changes of temperature, 
which expand or contract unequally the different parts of the 
telescope, by the weight of the instrument itself, which will 
bend it differently according to the different ways in which it 
may be pointed with respect to its support, or by the acci- 
dental jarring of this support, or of any part of the telescope. 
if a telescope is well made, its line of sight will keep its 
direction long enough at a time to allow correct measure- 
ments to be made by means of the marks used for that pur- 
pose, as already explained. 

487. All that can be seen through a telescope at once is 
said to be in the field of the telescope. The field is large or 
small, according to the size of the greatest angles between 
objects in the field. The field is generally only a few minutes 
of arc in width when an eye-piece of high magnifying power 
is used. 



246 Outlines of Astronomy. [Sec. 488. 



CHAPTER XL 

THE SPECTROSCOPE. 

488. In the ordinary use of a telescope, it is desirable that 
the light should pass through it with as little dispersion as 
possible. But when we wish to study the chemical pro] 
ties of distant objects, and not merely their shape and - 
we must begin by finding out what different kinds of light we 
receive from them. This can be done by making use of a 
prism, as we have seen (432). 

489. A prism made for the purpose of scientific research is 
usually a piece of glass having two plane refracting surfa 
which are not parallel with each other. The prism is 
placed that the light which is to be examined may fall on one 
of these surfaces and be retracted into such a dire< tion as to 
pass out of the prism by the second surface. By this pro- 
cess, the general direction of the light is usually made difl 
ent from that direction in which it came to the prism ; but 
if it is desirable to avoid this change of direction, it m,i\ 
avoided by means of total reflections or by the combination 
of prisms made of different kinds of glass (431, 433)- What- 
ever the general direction may be in which a beam of light 
leaves a prism, the different kinds of light in that beam will 
have been turned into slightly different directions by the 
refractions which the beam has undergone. That is, the 
beam will have been dispersed. Suppose it to have come 
through a round hole in the wall or in a metal plate placed 
before the prism. It will then be a round beam, and would 
make a round spot of light on a screen held perpendicular to 
it, if it had not been dispersed. But after passing through 
the prism it will no longer make a single round spot of light 
upon the screen, unless it happens to contain only one kind 
of light. In that case, the prism cannot disperse the light. 



Sec. 4S9.] The Spectroscope. 247 

Suppose, however, that there are two kinds of light in the 

n. Then, after passing the prism, the beam will be 

irated into two beams having slightly different directions, 

and therefore getting farther and farther apart as they go on 

beyond the prism. Each of these beams will be round, and 

trge as the whole beam was before it was dispersed ; but 

it will not be as bright as the whole beam, because it contains 

onlv part of the light which reached the prism. Now if a 

en is held close to the prism, it will cut off these two 

beams before they have fairly separated from each other, and 

the spot of light formed by one beam will partly overlap the 

spot formed by the other. If we move the screen away from 

the prism to a distance at which the two beams are wholly 

separated from each other, there will be two round spots of 

light on the screen. 

490. The directions of both the refracted beams will be 
perpendicular to the direction of the line which forms the in- 
tersection of the two refracting planes through which the light 
has passed, provided that the direction of the beam incident 
on the prism was perpendicular to this line. If the prism is 
made so that its two surfaces used in refraction come together 
and form an edge, then, supposing the edge to be horizontal 
and its direction to be perpendicular to that of the incident 
beam, one of the two spots on the screen will be over the 
other; if the edge is vertical and the incident beam is hori- 
zontal, the two spots will be on a level. 

491. If the two kinds of light differ very little from each 
other in refrangibility, the directions of the two refracted 
beams will be so nearly the same that they will not be sepa- 

1 from each other even at a great distance from the prism. 
In this case, we must bring the light to the prism through a 
narrow slit instead of through a round hole ; placing the slit 
with its long edges parallel to that Q(\\re of the prism win re 
refracting surfaces meet. The incident beam will 
then be tlat and thin ; the two refracted beams will also be 

and thin, and will soon be I lear of each other ; while if 
the slit had its long edges perpendicular to the intersection 



248 Outlines of Astronomy. [Sec. 491. 

of the refracting surfaces of the prism, it is plain that the 
thinness of the beam would be of no service (490). 

492. The light which has been dispersed by passing through 
a prism may be looked at with a telescope placed in its path, 
instead of being received upon a screen. The appearance it 
presents is called a spectrum, whatever method of examining 
it may be employed. The different kinds of light differ in 
color as well as in refrangibility. Blue light, for instano 
more refrangible than yellow, and yellow than red light. If a 
spectrum is formed by a beam which contains only three 
kinds of light, one blue, one yellow, and one red, the spec- 
trum will consist of a blue spot, a yellow spot, and a red spot. 
The shape of these spots will usually depend on the shape of 
the opening through which the light comes to the prism ; if 
this opening is a slit, the spots will be narrow strips of light 
But if the opening is large enough to allow us to see through 
it the whole of the surface from which the light comes, we 
shall then have a spectrum made up of three separate im \ 

of that surface ; one blue, another yellow, and the third red. 

493. Suppose, however, that instead of three kinds of light 
very different from each other in refrangibility and in color, 
the beam incident on the prism contains three kinds of light 
almost exactly alike in these respects ; three kinds of yellow 
light, for instance, all nearly of the same shade of yellow. In 
this case, if the light comes through a slit, the spectrum will 
consist of three narrow strips of yellow light, side by side, and 
close to each other. But if we let in the light through a 
larger opening, we shall not have, as before, three separate 
images of the object from which the light is sent out ; for the 
images will be so close together as to overlap, and will make 
a confused spot of yellow light 

494. The spectra of incandescent. solids and liquids consist 
of a great variety of kinds of light, each of which differs so 
little from those most like it that a spectrum formed by them, 
even when the slit before the prism is made very narrow, does 
not seem to be made up of separate strips of light placed side 
by side. Instead of this, each strip overlaps that next to it, 



Sec. 494.] The Spectroscope. 249 

so that the spectrum looks like a band of light Sometimes 
o{ a spectrum o\ this kind is so faint that its colors 
ear; generally, however, it is colored ; in either 
1 continuous spectrum. The width of this 
•rum depends on the size of the opening through which 
the light comes. If this opening is a slit, then the width of the 
trum depends on the length of the slit ; provided that 
apparent size oi the object from which the light comes is 
rable. But the spectrum of a star is narrow, whatever 
,/di the slit may have. The length of the spectrum de- 
pends on the shape of the prism, the material of which it is 
made, its distance from the place where the spectrum is ex- 
amined, and the difference of refrangibilitv between the liHit 
at one end of the spectrum and that at the other. The spec- 
trum formed by light sent out from any object is commonly 
carted the spectrum of that object. 

The spectrum of an ordinary flame is continuous ; for 
the brightness of the flame depends on the small solid particles 
of soot which are burning in it, rather than on the hot gas in 
:h they float. When a flame of this kind is bright enough, 
>pectrum is dark red at the end formed by the least retran- 
smit, and gradually changes through various shades of 
and orange to yellow in its middle portions. Beyond the 
yellow portion, the spectrum continues to change by degrees 
through different tints of green and blue. But ordinary flames 
are apt to send out more yellow and red light in proportion to 
that which is green and blue than a beam of sunlight does. 
The spectrum of sunlight, at that end formed by the most 
rible light, has a violet color ; so that it seems as if it 
re on the point of becoming red again when it ends. Cer- 
chemical effects, which can be produced more readily in 
blue an<; , in in red or even in yellow light can also be 

yond the violet end of the spectrum. It 

then, that the spectrum does not absolutely end where it 

. but that there are certain rays, which hue 

been called invisible actinic rays, 11 le than those 

which form violet light. In like manner, certain effects of 



250 Outlines of Astronomy. [Sec. 495. 

heat, which can be more easily produced in red than in blue 
light, can be produced beyond the red end of the spectrum. 
This gave rise to a theory that there are three spectra partly 
overlapping each other, only one of which could be seen ; but 
recent researches have shown that there are serious objec- 
tions to this theory. The proper explanation of the matter 
has not yet been fully settled. 

496 The spectrum of sunlight is not perfectly continuous, 
when formed by a sufficiently narrow slit ; it is crossed by 
numerous dark lines. To account for these lines, we must 
consider the properties s with respect to light Under 

certain conditions, an incandescent or phosphorescent 
may send out light which forms a continuous .spectrum ; 
under other conditions, its spectrum may be discontinuous ; 
in other words, when a sufficiently narrow slit is used, the 
spectrum may be made up of - light, usually 

called bright lines. Now when light which would otherwise 
form a continuous spectrum comes through a gas on its way 
to the prism, this gas being not too hot compared with the 
body to which the continuous spectrum belongs, a curious 
effect is produced. The continuous spectrum i- I by 

dark lines at just those places where bright lines would have 
been seen if the spectrum of the gas itself, in an incandescent 
state, had been observed instead of the spectrum of the body 
behind the gas. That is, a gas absorbs light of the same 
refrangibility with that which it is itself capable of sending 
out. A gas may be bright enough to have a discontinuous 
spectrum of its own, and may yet absorb particular kinds of 
light from a brighter object behind it. 

497. Now whatever the Sun may be made of, the spectrum 
of its photosphere (32) is continuous, while the gases enclos- 
ing the photosphere, and forming the various portions of the 
Sun's atmosphere, absorb particular kinds of the light which 
the photosphere sends out. For instance, there is much 
hydrogen in the Sun's atmosphere. One of the bright lines 
of the spectrum of incandescent hydrogen is of a particular 
shade of red; and in the spectrum of sunlight there is a 



.17-] The Spectroscope. 251 

strong dark line just at the place where that particular shade 
of red would come in a perfectly continuous spectrum. The 
other bright lines of the spectrum of hydrogen also have 
dark lines answering to them in the spectrum of the Sun ; 
and so it is with many other kinds of matter besides hydrogen 
A metal may be made to give a spectrum of bright 
lines by passing strong electric sparks between the ends of 
res made of the metal. In this way we learn what the 
ctrum of a metal would be if the metal were gaseous in- 
stead of solid ; and when we find in the spectrum of sunlight 
irk lines answering to the bright lines of any metallic spec- 
trum, we conclude that the metal to which that spectrum 
belongs is in the Sun's atmosphere, and reduced to a gas by 
the heat around it. 

498. The spectrum formed by light which has passed 

through certain gases and liquids shows dark bands, 

icier than the dark lines just mentioned. Any band of 

this kind shows that light of many degrees of refrangibility 

differing little from each other has been absorbed by the gas 

or liquid lying between the prism and the body which is giv- 

g out light. Having learned what particular bands or lines 

any medium produces in the continuous spectrum of an 

object behind it, we can then tell by the appearance of a 

spectrum whether that medium lies between us and the body 

which gives out the light we are examining. In these ways, 

and in others like them, we can study the chemical properties 

of bodies at a distance from us (9). Occasionally, too, we 

>me thing of their density and heat; for the lines 

hange their width and appearance to some extent 

J according to the md heat of the gases to which these 

. lines are due. The opinions which now prevail respecting 

j the structure of the fixed stars (95) depend on observations 

I of this kind. For instance, the hydrogen lines in the 

) spectrum of Sirius are dark and wide ; hence greatly COn- 

I denied hydrogen i.^ thought to abound in the atmosphere of 

Sir 

499- When a line appears in any spectrum very near the 



252 Outlines of Astronomy. [Sec. 499. 

place where such a line would have been expected to appear, 
but not exactly in that place, the explanation of the appear- 
ance usually given is that the body producing the observed 
line is in motion with respect to the observer. Thus 
hydrogen line in the spectrum or Sirius has been thought to 
be a little less refrangible than the corresponding line in the 
spectrum of the Sun ; and this appearance has been thought 
to show that the distance between Sirius and the Solar S 
tern is rapidly increasing (94). But this explanation is 
thought to be incorrect by some of the few people who know 
enough to make their opinions on the subject worth havi 
Those who have not thoroughly studied the science of optics 
cannot understand the arguments in favor of the explanation 
just mentioned or those against it ; although they may easily 
fancy that they understand them. 

500. Lines id the spectrum of the Sun, or in the spectra of 
its prominences, are sometimes seen curiously bent one way 
or the other; and these observations, too, are thought by 
some, but not by all, astronomers to show that certain mi 
ments take place in the Sun's atmosphere (70). 

501. The name of spectroscope may be given to any 
instrument intended to be used in forming and studying any 
kind of spectrum. The only indispensable part of a spectro- 
scope, then, is a prism or some other contrivance for dis- 
persing light. But the spectroscopes most frequently u 
have many other parts. One of these parts is a slit placed 
before the prism, and so made that it may be opened or 
closed as far as seems desirable. Before the prism there are 
also lenses intended to put the light which comes to the 
instrument into the form of parallel pencils. Behind the slit 
and prism is a little telescope with which the spectrum may 
be examined. There must also be some measuring apparatus 
for determining the place of each line in the spectrum with 
respect to other lines either of the same or of another spec- 
trum. In studying the spectra of stars, a piece of glass called 
a cylindrical lens is used to make the spectrum wider than it 
would otherwise be. 



Sec. 502.] The Spectroscope. 253 

502. When a long spectrum is wanted, a considerable 
number ot prisms must be used. In going through these 
prisms, the general direction of the light is often much 

inged. In fact, the beam of light which enters the instru- 
ment is sometimes carried round in a ring through several 
sms, until it has got back nearly to its old direction ; then 
jcted and sent the other way through the same ring of 
prisms before it is allowed to come out into the tube where it 
oserved. By apparatus of this kind, the light may be 
icted twenty or thirty times, becoming more and more 
dispersed at each refraction. If it is so much dispersed, 
only a little of the spectrum it forms can be seen at once. 
This makes it necessary to contrive means for bringing any 
particular part of the spectrum into view, and at the same 
time setting the prisms so that they may act to the best 
advantage on that particular part. A spectroscope fitted 
with suitable contrivances for doing this is called an auto- 
;c spectroscope. 

503. When the shape of one of the Sun's prominences is 
to be observed by means of a spectroscope (66), the slit is 
opened enough to allow the whole prominence to be seen 
through it (492), and that part of the spectrum which con- 
tains some particular line in the spectrum of the prominence 
is brought into view. The red line of hydrogen (497) is usually 
chosen for this purpose. There is now a red image of the 
prominence in view, and also a confused spectrum of sunlight 
reflected from the Earth's atmosphere, or from its liquid and 
solid contents. But this confused spectrum has been made 

, fainter by the dispersion of its light in its passage through 
1 the prisms of the spectroscope : while as the reel light of 

hydl all of one kind, it is merely separated farther 

I and fart' • through the prisms, from the rest 

. of the V- . • out by the hydrogen and by the other kinds 

of matter in the prominence. The more the Spectroscope 
1 disperses light, therefore, the fainter is the light among 
I which the prominence appears, compared with the light of 

the prominence itself. I if we have a sufficiently 



254 Outlines of Astronomy. [Sec. 503. 

powerful spectroscope, we may easily see the shape of any 
part of the chromosphere. 

504. During a total eclipse of the Sun, a spectroscope used 
without a slit will give several distinct and differently col- 
ored images of the brighter part of the light then seen around 
the Sun ; for the spectrum of this light is discontinue 

496), the Sun's atmosphere being largely made up of in( 
descent gases. 

505. For astronomical purposes, spectroscopes are usually 
attached to telescopes. The eve-piece of a telescope is taken 
off when the spectroscope is to be used with the telescope, 
and the spectroscope, with its various lenses, is put in the 
place of the eye-piece. This combination of telescope and 
spectroscope has been called a telespectroscope ; but this 
name is little used. 

506. A direct vision spectroscope is one in which the light 
is dispersed without much change in its general direction 

( 4 3 9 ). 



Sec. 507.] Practical Astronomy. 255 



CHAPTER XII. 

PRACTICAL ASTRONOMY. 

507. The practical work of all astronomers must chiefly 
consist in measuring angles ; for we can study celestial 
objects only by means of our eyes, and can never come near 
enough to them to handle, measure, and weigh them as we 
do the terrestrial objects which we study. All that we can 
do in the measurement of celestial objects is to measure 
visual angles (,452) between different points of the same 
object, or between a point in one object and a point in 
another. 

508. The great use of the magnifying power of a telescope 
is to enable us to measure, more accurately than we other- 

>e could, the small visual angles between points nearly in 
a line with each other as seen from the Earth. The fixed 
stars, which include most of the celestial objects usually in 
sight (21, 26), are made to appear smaller, rather than larger, 
by the use of telescopes in observing them (80). But the 
visual angles between them may be magnified, as we have 
seen (89, 91). 

509. The distance of any object from the Earth can only 
be determined by observations of parallax (357, 450) ; and 
accurate observations of parallax consist in the measurement 

ifferent places or times of certain small visual angles. 

The distance between any two celestial objects cannot usually 

known unless we first know the distance of both of them 

from the Earth ; and never can be known if we cannot learn 

the distance of either of them from the Earth. Our knowl- 

of any celestial object also depends 

our knowledge of its distance. All astronomical mcasurc- 

then, must be obtained by calculation from measured 

visual ar._ 



256 Outlines of Astronomy. [Sec. 510. 

510. It is found convenient in practice to measure many 
visual angles by finding the time during which bodies change 
their directions from the place of observation by amounts 
equal to the angles which are to be measured. We have 
seen, for instance, that the apparent diameter of the Moon 
may be measured by the time required for the passage of a 
thread across the disk of the Moon (484). 

511. It is also frequently found convenient to substitute 
arcs for visual angles (410). We usually regard ourselves 
as living beneath a dome-shaped surface which we call the 
sky (259). In the practical work of astronomy, we take ad- 
vantage of this natural way of looking at the universe, in 
order more readily to keep in mind what angles we are 
considering. But, for the sake of accuracy, we speak of the 
celestial sphere rather than of the sky. This celestial sphere 
has its centre wherever the observer is, or supposes himself 
to be. How far off from him its surface is placed is a matter 
of no consequence, so long as all parts of that surface are 
understood to be equally distant from the observer's place. 
A celestial sphere a foot in diameter, with its centre at a 
point about the middle of the observer's eye, will answer the 
purposes of astronomy as well as one large enough to take in 
all the known universe. But perhaps the easiest way of un- 
derstanding the celestial sphere is to regard its surface as 
beyond every object that can be discovered. 

512. Wherever we place this surface, we regard all the 
celestial objects as projected upon it (270), the point of sight 
being always at the centre of the sphere. We may then 
replace the visual angle between two objects by the arc of a 
great circle of the celestial sphere (412), passing through 
the projections of the two objects. The apparent distance 
between the objects is accordingly the amount of rotation 
answering to the arc thus defined. This will be plain to any 
one who takes the trouble to get a clear understanding of the 
meaning of great circles, arcs, and angles. A less accurate 
way of explaining apparent distances on the celestial sphere, 
but one which makes it easier to get a rough notion of them, 






Sec. 512.] Practical Astronomy. 257 

is that the apparent distance between two stars is the frac- 
tion of the whole distance round the sky formed by a line 
drawn along the sky as directly as possible from one star to 
the other. 

513. In order to measure arcs upon our imaginary celestial 
sphere, we find it well to choose certain points and circles 
upon its surface from which we may afterwards measure. 
Our choice will evidently depend to a great extent on the 
place where the centre of the sphere is -supposed to be. 
Three suppositions with regard to this centre are in common 
use by every astronomer. 

514. First, the centre of the celestial sphere may be 
; irded as at some point near the surface of the Earth, this 

point, for any particular observation, being in the instrument 
with which the observation is made. Secondly, in many 
calculations, it is convenient to suppose the Earth's centre 
(157) to be the centre of the celestial sphere. When we 
speak of the geocentric place of any object, we mean the 
place of its projection on the surface of a celestial sphere, 
the centre of which is at the Earth's centre. Thirdly, in 
other calculations, the most convenient centre for the celes- 
tial sphere is the centre of the Sun. The heliocentric place 
of any object is the place of its projection on the surface of 
a celestial sphere with its centre at the centre of the Sun. 
When the place, or the apparent place, of an object is 
spoken of by astronomers, they often mean its geocentric 
place ; at other times, they mean the place of its projection 
on the surface of a celestial sphere with its centre somewhere 
on the Earth's surface ; the exact place of this centre depend- 
ing on the place and kind of the observations which are 
under consideration. It usually makes little difference in the 
place of a celestial object whether we suppose the centre of 
the celestial sphere to be in one terrestrial place or another. 

515. We can now give more exact meanings than we pre- 

- ould to some of the astronomical terms which we 
have had to use. The zenith and nadir, for example, are 
the points where the surface of the celestial sphere is pierced 

17 



258 Outlines of Astronomy. [Sec. 515. 

by the vertical line (252) which passes through the point 
chosen for the centre of the sphere. The nadir is that one 
of these points which lies in the same direction with the 
Earth's centre from the centre of the celestial sphere : the 
zenith lies in the opposite direction. Hence, if we place 
the centre of the celestial sphere at the centre of the Earth, 
we can have no zenith or naciir. 

516. The horizon is the great circle of the celestial sphere 
formed by the intersection of its surface with a plane passing 
through its centre and perpendicular to the vertical line (412) 
The plane of the rational horizon is parallel to the plane 
the horizon just described, and passes through the centre 
of the Earth (264). No two places can agree in the planes 
of their horizons; but if they are in the same vertical line, 
the planes of their rational horizons will be the same. The 
zenith and nadir are the poles of the horizon (412). 

517. The meridian is the great circle of the celestial 
sphere formed by the intersection of its surface with a plane 
containing both the vertical line and the Earth's axis. 
Hence different places may have different meridians; but 
two places, equally far from the Earth's centre, may agree in 
the planes of their meridians, although their vertical lines 
must differ. The intersection of the meridian plane of any 
terrestrial point with the Earth's surface may be called the 
terrestrial meridian of that point. But in fact, its meri< 

on the celestial sphere is the meridian by which its longitude 
is reckoned, as we shall s< 

518. The prime vertical is the great circle of the eel 
sphere formed by the intersection of its surface with a plane 
containing the vertical line, and perpendicular to the plane of 
the meridian. 

519. The points where the meridian crosses the horizon 
are the north and south points ; those where the prime vertical 
crosses the horizon are the east and west points ( 

520. All great circles of the celestial sphere which contain 
the vertical line are vertical circles. The angle between the 
planes of any two vertical circles is a difference of azimuth ; 



Sec. 520.] Practical Astronomy. 259 

and the arc of the horizon lying between these planes is an 
arc answering to this angle, and signifying the same amount 

of rotation (410). The azimuth ot any object is the angle 
between the meridian plane and the plane of the vertical 
circle pass £h the projection of the object on the 

surface of the celestial sphere. In other words, the azimuth 
t is the arc of the horizon lying between the north 
or south point (as the case may be) and the point where the 
horizon is crossed by the vertical circle on which lies the 
projection of the object. Amplitude is the difference of 
azimuth between the east or west point and any object which 
is rising or setting. 

521. The zenith and nadir are points belonging to every 

vertical circle, and accordingly have no azimuth ; or, if we 

choose, we may consider them as belonging to any particular 

ical circle, and as having the same azimuth with any 

n point in that circle. Any point in the prime vertical 

has an azimuth of 90 . 

Since all points in any particular vertical circle have 
the same azimuth, we must know more than the mere azimuth 
of a point before we can settle its place on the celestial sphere. 
If a line is drawn from the centre of the sphere to the point 
the place of which is to be determined, the angles between 
s line and the vertical line are the zenith distance and 
the nadir distance of the point. Either of these angles will 
serve our purpose, but the zenith distance is the angle most 
frequently used. The arc answering to zenith distance be- 
longs of course to a vertical circle, and reaches from the 

• zenith to the point the place of which is to be determined. 

The arc of the same circle extending from this point to the 

• /on is the altitude of the point When we know the 

azimuth and zenith distance of a point, or its azimuth and 

1 alt ' can find the point on the celestial sphere if we 

are I lUth. For instance, if 

I the altitude of a poii and its azimuth 90°, it must be 

in the prime . from the horizon to the zenith. 

Hut tin : and the other west of 



260 Outlines of Astronomy. [Sec. 522. 

the zenith. If we are told, however, to begin reckoning azi- 
muth at the south point, and go towards the north through 
the west, we know that the point we arc to find L that v. 
of the zenith. The azimuth of the other point would be 270 
instead of 90 . 

523. When altitudes are reckoned from the horizon to 
points below it, the negative sign of algebra is placed be- 
fore the figures denoting altitude. Thus any point the alti- 
tude o( which is — 40° has a zenith distance of 130 ; for the 
zenith distance of the horizon is 90 . and the point is 40 
farther than the horizon from the zenith. 

524. The Earth's rotation constantly changes the places 
of all the circles just described among the projections of the 
celestial objects ; but if we choose, we can regard the cin 

as stationary and the projections as having a retrograde m 
men! across them (125). This movement is commonly ca 
the diurnal movement of the stars and other celestial obj< 
The diurnal movement, as observed from either of the Earth's 
poles, is only a movement in azimuth ( 2 S 1 ) ; but 
from any other terrestrial place, it is a movement both in 
muth and in altitude. 

525. One of the various meanings of the word transit is 
passage across a circle of the celestial sphere (32 

We speak, for instance, of the transits of si the 

meridian or over the prime vertical ; and instruments meant 
for observing the times at which these transits happen are 
called transit instruments. Meridian transits are also (ailed 
culminations. Every star crosses the meridian twice while 
its diurnal movement carries it once round the Earth. Th< 
two culminations are called the upper and lower culmina- 
tions of the star. If it is one of the stars which never set at 
the place where it is observed (124. 2S5), both its culmina- 
tions will be in view ; otherwise its lower culmination will 
take place below the horizon. 

526. If we now consider the centre of the celestial sphere 
to be at the Earth's centre (514), so that we can have no 
vertical line, the line of the Earth's axis will naturally be the 



Sec. 5^6.] Practical Astronomy. 261 

chief line to be used in our measurements. The points where 
ierces the surface of the celestial sphere may be called the 
celestial poles, or simply the poleF. The great circle of the 
celestial sphere ot which these points are the poles (412) is 
the celestial equator, or the equinoctial ; but it is usually 
ed simply the equator. Its plane is evidently the same 
the plane of the terrestrial equator. The great circles of 
the celestial sphere which pass through both poles are so 
often spoken of as meridians that this name for them cannot 
be called incorrect, although, at the outset of works on prac- 
tical astronomy, they are usually called hour circles, or 
circles of declination. They differ from the meridians 
already described (517) in not being carried about by the 
Earth's rotation. The angle between the planes of the 
meridians of any two terrestrial places is the difference of 
the longitudes of those places, as we learn by the study of 
geography ; the angle between the planes of two hour circles 
called a difference of right ascension. The angle be- 
tween two lines, one of which is the intersection of the plane 
of the equator with that of the meridian of some terrestrial 
place, while the other passes through that place and through 
the Earth's centre, is the latitude of the place. The angle 
between two lines, one of which is the intersection of the 
plane of the equator with that of an hour circle, while the 
other passes through some point in that circle and through 
the centre of the celestial sphere, is the declination of the 
% point. The meanings of longitude and latitude, right ascen- 
sion and declination, are more easily understood when they 
are explained by means of arcs than when explained by means 
of angles ; but it must be remembered that they are not dis- 
titude of a city, for instance, is not the dis- 
tance in miles between some point in that city and the nearest 
point on the equator ; it is the angle between the vet 
lines of these two points, or the frai tion of a meridian lying 
between these vertical lines, no matter how fir from the 
centre we place the surface of the sphere on which 
the meridian to be drawn. In reckoning latitude 



262 Outlines of Astronomy. [Sec. 526. 

accurately, we take into account the fact that vertical lines 
do not always pass exactly through the Earth's centre (253). 
It is easy to see that the declination of a star is not a dis- 
tance, because we cannot measure in miles on the cele> 
sphere as we can upon the Earth ; when we say that a 
is in 20 north declination, we obviously mean that the arc 
of the hour circle passing through the projection of the si 
and measured northwards from the equator to this projection, 
is one-eighteenth of the whole circle, whether the extent of 
that circle is considered as only a few feet, or as millions of 
times greater than the distance of the most remote stars from 
the Earth (410). For the whole circle contains 360 ; and 
20 is ^| of 360. 

527. North polar distance (which, like zenith distan 
merely angular distance) may be used in stating the pi 
of stars when it is thought more convenient than declination. 
Thus, the north polar distance of a star is 130° if the star is 
in 40 south declination, or, as it may be expressed, if the 
declination of the star is — 40 (523). 

52S. Suppose that the place of the whole celestial sphere, 
with its poles, equator, and hour circles, as just described 
changed by rectilinear motion (40S), so as to carry its centre 
to some place near the surface of the Earth. The sphere 
will now coincide with the celestial sphere of that pi 
The meridian of the place, which may be called the local 
meridian, will be brought by the Earth's rotation to coinci- 
dence with one after another of the hour circles (or celestial 
meridians) ; or, if we please, we may consider the hour circles 
as having a diurnal movement (524). If the place selected is 
one of the Earth's poles, the equator will coincide with the 
horizon and the vertical line with the axis. If it is a place 
on the Earth's equator, the poles will coincide with the north 
and south points, and the equator will pass through the zenith. 

529. Any change in the right ascension and declination o( 
celestial objects produced by the shifting of the celestial 
sphere in the manner just supposed is an effect of parallax 
(357)* The most usual meaning of parallax is the angle 






Sec. 5 Practical Astronomy. 263 

between the lines pointing to an object from the Earth's 
re and from the place for which the parallax of that 
terminecl. It" the object is in the zenith it 
will have no parallax ; it" on the horizon, its parallax will be 
^reat as possible. The parallax oi an object on the hori- 
zon is its horizontal parallax. If the place of observation 
irth's equator, it will be as far as any terrestrial 
place from the centre of the Earth (159). Hence the hori- 
zontal parallax oi an object is greatest when the object is 
viewed from some place on the Earth's equator ; this paral- 
lax is equatorial horizontal parallax, and is often what we 
mean when we use the word parallax by itself. The com- 
parison of the apparent places of an object observed at about 
the same time in different parts of the Earth will show the 
difference of its parallaxes at the stations from which it was 
observed. If this difference is noticeable, we may derive 
from it the equatorial horizontal parallax and the distance of 
the object. 

530. The hour angle of any celestial object is the angle 
between the plane of its hour circle and that of the local 
meridian, at some particular time and place. 

531. When the centre of the Sun is taken as the centre of 
the celestial sphere, the ecliptic is usually considered to be 
the principal circle of that sphere. We are now able to 

ine the ecliptic more exactly than we could before (322). 
It is the great circle formed by the intersection of the plane 
of the Earth's orbit (139. 143) with the surface of the celes- 
tial sphere. The poles of the ecliptic are the points where 
the surface of the celestial sphere is pierced by a line drawn 
through its centre perpendicular to the plane of the ecliptic. 
This line may be call' is of the ecliptic. The great 

igh both poles of the ecliptic arc called 
Tea of latitude, and th their planes are 

-differences of longitude, while arcs of 
of latitude extending either way from the ecliptic, or the 

latitudes. Celes- 
tial s and latitude the terrestrial angles 



264 Outlines of Astronomy. [Sec. 53 r. 

of the same names in being measured on the ecliptic and the 
great circles passing through the poles of the ecliptic, inst 
of on the equator and the meridians. 

532. We may now again consider the celestial sphere to 
be shifted by rectilinear motion so that its centre ma\ be 
brought from the centre of the Sun either to the Earth's 
centre or to some part of its surface. The sphere will then 
coincide with the celestial sphere of the place to which its 
centre is thus removed. The great circle of the sphere called 
the ecliptic will lie in a plane parallel to that which we have 
hitherto called the plane of the ecliptic (139), if not actually 
in that plane. This change of plane, if any occurs, will make 
little difference in the latitudes of the stars, or of any celestial 
objects except those near the Earth. Even the longitudes 
the stars will not be noticeably altered by the change. o\i 
to their gre.it distance, which mikes the parallax of even the 
nearest of them hardly perceptible ; the parallax of a star be- 
ing the angle between the lines drawn from it to the Sun and 
to the Earth. But the longitude of any object between the 
Sun and the Earth must be changed 1S0 when the centn 
the celestial sphere is carried past it. Suppose, for instance, 
that the centres of the Sun, Mercury, the Earth, and M 
are at some one time in the plane of the ecliptic. Men 
being between the Sun and the Earth, and the Earth betw< 
Mercury and Mars. Then, if the Sun's centre is the centre 
of the celestial sphere, the longitudes of Mercury, the Earth, 
and Mars will all be the same ; if the celestial sphere is 
shifted so as to bring its centre to coincide with that of the 
Earth, this change will leave the longitude of M 
and will place Mercury in the opposite longitude, w! 
the Sun will be placed. The longitude and latitude which, 
when taken together, determine the heliocentric place (514) 
of any body, are its heliocentric longitude and latitude ; 
and its geocentric place may be shown either by its geocen- 
tric longitude and latitude, or by its right ascension 
declination. As we have seen, geocentric and heliocentric 
latitude may differ somewhat, and geocentric and heliocentric 



Sec. 532.] Practical Astronomy. 265 

Jtude considerably. When the centre of the sphere on 

ch longitude and latitude are reckoned is supposed to he 

at the Earth's surface, the longitudes and latitudes of objects 

tly near the Earth will differ slightly by the effect of 

parallax (529) from their geocentric long ind latitui 

In reckoning azimuth, right ascension, or longitude, 

some point for the beginning of our reckon- 

The point chosen for this purpose in reckoning azimuth 

ither the north or the south point of the horizon (522). 

and longitude begin at the vernal equinox, 

h we can now define more exactly than we previously 

coir Since the planes of the ecliptic and equator do 

not coincide and both pass through the centre of the celestial 

sphere, they must intersect each other in a straight line, 

called the line of the equinoxes, which pierces the surface 

of the celestial sphere in two opposite points, where the 

equator and ecliptic cross each other. The Sun's centre is 

I at or near one of these points at the time of the 

juinox (301) ; hence the point itself is often called 

vernal equinox, although some writers prefer to call it 

the first point of Aries. 

The right ascension of any object may be denoted 

the arc of the equator beginning at the vernal equinox 

and £ the course of any thing supposed to have direct 

* the equator to the point where it crosses the 

r circle passing through the object. As there are two of 

•• points, that point is chosen from which the declination 

the object sured ; in other words, the point which 

in 90 of irele from the object. 

535. The longitude of any object is measured from the 

the ecliptic, following the course of any 

thing >ed to have direct motion in the ecliptic, to that 

point crossed by the circle of latitude through the 

which the angular distance, or latitude of 

than 90 . 

5 3 r < llust rations will be of service in clearing up 

the meaning of these Statements. Let us suppose that at 



266 Outlines of Astronomy. [Sec. 536. 

some moment when the vernal equinox has just come to coin- 
cidence with the west point of the horizon, the centre of the 
Moon has just come to its upper culmination ^525). The 
line of the equinoxes is now perpendicular to the plane of 
the local meridian (52S), and this local meridian, tl 
has the equinoxes tor its poles (412;. Hence, if any ureat 
circle passing through the equinoxes is considered as cut in 
halves by the line of the equinoxes, either half of it will now 
be cut in halves by the local meridian ; so that one-fourth, or 
90 , of the whole circle will lie between either equinox and 
either of the points where the circle crosses the local meridian 
(just as one-fourth of the local meridian itself lies between either 
pole and the equator). Both the equator and the ecliptic 
are great circles passing through the equinoxes. Hence 9x5° 
of the equator and likewise 90° of the ecliptic lie at this 
moment between the west point of the horizon and the I 
meridian. The local meridian coincides with the meridian 
(or hour circle) of the Moon's centre ; and it also coincides 
with the circle of latitude passing through the Moon's centre. 
For the poles of the equator always lie on the local merid- 
ian ; and when the equinoxes are on the horizon, the p 
of the ecliptic must also lij on the local meridian ; or else 
each of these poles would be nearer one equinox than the 
other. We must measure right ascension and longitude the 
contrary way from that in which celestial object- tied 

by their diurnal motion. As we have seen, this will make 
the right ascension of the Moon 90 , and its longitude 
also 90 . 

537. If the Sun is at this time just passing its lower culmi- 
nation (525). its right ascension and geocentric longitude are 
270 ; for although it is, like the Moon, in the plane of the 
local meridian, we must not end our measurements 01 
right ascension and longitude at the points where we stopped 
in the example already given. If we measured from the 
Moon's centre either way along the local meridian tow.: 
the Sun, we should not reach it until we had passed through 
one of the poles of the equator, and likewise through one of 



Sec. 537.] Practical Astronomy. 267 

the poles of the ecliptic. We must therefore (534, 555) 
e three-quarters of the way round either the equator 

or the ecliptic, beginning at the vernal equinox, in order 
the right ascension and longitude of the Sun ; and 

three-quarters of 360 is 270 . 

If we wish to find the declination of the Moon at its 
ulmination, we must measure the angle between two 
lines drawn from the centre of the sphere, one to the Moon's 
centre, and the other to the nearest to the Moon of the two 
points where the eqmtor crosses the meridian. In the ex- 
ample already given, let us suppose this angle to be 20 ; or, 
which amounts to the same, let us suppose that the arc of the 
il meridian, one end of which is at the projection of the 
>n , s centre and the other at the nearest point of the equa- 
l's one-eighteenth of the whole meridian. Let us now 
inquire whether the Moon is north or south of the equator, 
and also what its geocentric latitude must be. 

ig the equinoxes, when they are on the hori- 
the poles of the local meridian, we may measure the 
>etween the planes of great circles passing through 
the equinoxes by means of arcs of the local meridian, just as 
we measure angles between the planes of meridians or of 
hour circles by means of arcs of the equator. Now the angle 
between the planes of the equator and ecliptic is about 23^° 
(166). Hence the arc of the local meridian lying between the 
equator and ecliptic is 23^°, or rather less than one-fifteenth 
of the whole meridian, whenever the equinoxes are on the 
horizon. Moreover, if the vernal equinox is on the western 
zon, the first half of the ecliptic, measured from the vernal 
- north of the equator (324). Now the plane of 
irbit is inclined only about 5 to the plane of the, 
j ecliptic (176). Accordingly, the arc of the local meridian 
bet I projection of the Moon's centre and the ecliptic 

can never be large ; it will be at its largest when the Moon 
culminates, and. at the same time, the point the pro- 

ject s the ecliptic come to the horizon. 

n then the arc will be only a jusl as the arc of 



268 Outlines of Astronomy. [Sec. 539. 

the local meridian between the equator and the ecliptic is 
only about 23^° when the equinoxes are on the horizon, and is 
less at other times. 

540. It seems, then, that in the case we have supposed, the 
Moon's declination is 20 north and not south of the equator; 
for as the ecliptic crosses the meridian about 23J north of 
the point where the equator crosses the meridian, the M 
would be about 43^° from the ecliptic if it were 20° south of 
the equator. The Moon's latitude is evidently about 3^° south. 
These facts may be also stated as follows : At the time 
our supposed observation the Moon's right ascension is 90 
and its declination +20 ; its longitude is 90 and its lati- 
tude —3.1°. If we wish to state its geocentric place a< 
lately, we must calculate the effect of parallax in altering its 
declination and latitude. Its right ascension and longitude 
will still be <jo° each. In other words, it will remain in the 
plane of the local meridian if the centre of the celestial spl 

is moved to the Earth's centre ; for the Earth's centre is itself 
in the plane of the local meridian. 

541. The longitude and right ascension of a celestial ol 
will not usually be equal to each other, as in the examples just 
given. But the spherical triangle having its angles at the 
object, one pole of the equator, and one pole of the eclit 
will enable us to determine the longitude and latitude of the 
object from its right ascension and declination, or these last 
from its longitude and latitude. By means of similar trigono- 
metrical calculations, if we know the a/i ninth and altitude 

an object, and those of the vernal equinox, we can determine 
the right ascension and declination, as well as the longitude 
and latitude, of the object. The place of the vernal equin 
however, cannot be directly observed : it has to be found 
from an extensive series of observations of the Sun and st 
as will presently be shown. When an object is crossing the 
meridian its declination is merely the difference between 
its zenith distance and the latitude of the place of observa- 
tion. It must be remembered that the words longitude and 
latitude are used in different senses according to their appli- 



54*.] Practical my. 269 

>n to ter: ; but both kinds 

g :ude and laiiiude are measured on the celestial sphere 

For instance, the latitude of a terrestrial place may 

be regarded - ; of the local meridian lying between the 

zenith and the equator (526). In other is the zenith 

• nee of the poin: the local meridian crosses the 

equator. Hence terrestrial latitudes may be learned from the 

is declinations may be learned from 

terrestrial latitudes. If the declination of a star is 3° north, 

and it c: 2 meridian 12° south of the zenith, then the 

ude of the place of observation is 15 north. When ac- 

s required, we must take refraction into account (262). 

All this becomes evident when we remember that at either 

pole of the Earth the equafor coincides with the horizon and 

one of its poles with the zenith ; while this pole approaches 

the horizon as we go farther towards the equator. It also 

appears that the altitude of the pole is equal to the zenith 

mce of the nearest point on the equator, and hence to 

the latitude of the place of observation ; for the arc of the 

dian from the pole to the equator is 90 . and the arc of 

the meridian from the zenith to the north point of the horizon 

so 90 . Hence if we take from each of these arcs the 

arc between the zenith and the pole, the remainders will be 

equal ; one of them being the zenith distance of the hie 

point on the equator, and the other the altitude of the pole. 

The zenith distance and the altitude of the pole may be found 

pretty accurately by observations of a star near the pole at 

both its culminations, even without any knowledge of its 

ination. We may thus obtain the latitude of some ter- 

-ial place. This latitude may be used in determining 

declinations ol nd may itself be corrected by the 

parison of a sufficient number of observations depen 

on it. 

In determining terrestrial longitudes, we make use of 
the Earth's rotation to measure ou: nd exprc 

-tead of l m in ar The 



270 Outlines of Astronomy. [Sec. 543. 

rotation of the Earth is a movement more nearly uniform 
(120) than any other which we know of. Accordingly, if 
meridians could be drawn so as to be visible on the celestial 
sphere, the best possible clock for us to use would be the 
Earth itself. The local meridian of any particul 
would answer for the hand of the clock, and the hour circles 
for the marks on its dial-plate. This clock, however, would 
not keep time with the Sun nearly enough for ordinary use 
(310, 311), although mean time clocks could be regul 
by means of it. 

544. In practice, when we wish to use the Eardi as a 1 
we have to place some kind of pointer in the plane of the 1 
meridian to serve for a hand, and then use the stars for marks 
on the dial-plate. The line of sight through a tel< 
the most accurate pointer we can use. But since the appar- 
ent movements of the si rendered slightly variable 
by the various real movements of the Earth about its centre 
(165), and since, moreover, the 

among each Other (93), our observations of their transits do 
not directly measure the passage of time as accurately . 
desirable. We can find, however, by calculation from t! 
observations, the moments when the local mer 
with the meridian passing through the vernal equinox. The 
interval between one of these moments and the next but 01 
called a sidereal day. Since the vernal equjnox is no actual 
object, but merely an imaginary point (533) determined by 
calculation, it follows that we might arrange our calculations 
so as to divide time into sidereal days of exactly equal length. 
But we could not be sure, after all. that one sidereal day 
would be exactly equal to another, unless we knew the rota- 
tion of the Earth to be a perfectly uniform movement; and 
probably it is not perfectly uniform. Astronomers have not 
thought it worth while to attempt to make all sidereal days 
exactly equal in length, but have contented themselves with 
making sidereal days much more nearly of equal length than 
are the days measured by the best artificial clocks. The 
place of the vernal equinox must be reckoned in such a man- 



Sec. 544.] Practical Astronomy. 271 

ner that it may nearly coincide with the actual place of the 
>n of the Sun's centre on any oi the occasions when 
the Sun is actually passing through the plane of the equator 
from south to north. If the vernal equinox were regarded as 
ith respect to any stars the proper motions of which 
are too small to be perceptible, it is obvious that the 
nal movement would soon carry the equator 
iy from this fixed equinox, while the ecliptic would also 
1 illy carried away from it by the change in its plane 
. We might, however, regard the equinox as having a 
perfectly uniform retrograde movement along the celestial 
equator, without making its place very different from that 
indicated by observations of the Sun, at any given time be- 
tween the earliest and the latest recorded astronomical obser- 
v>ns. But in practice, we regard the retrograde movement 
of the equinox, and hence the length of the sidereal day, as 
tly variable. 
545. We must now distinguish between two points called 
the mean and the trus equinox. The mean equinox retro- 
.: a rate which is meant to be proportional to that of 
the Earth's precessional motion, nutation being disregarded. 
>nal motion is known to be very nearly, but not 
quite, uniform ; hence, if we reckoned sidereal days by the 
culminations of the mean equinox, these days would be 
aim tly equal. It is considered best, however, to 

reckon sidereal days by the culminations of the true equi- 
.. in calculating the place of which, nutation, as well as 
precession, is taken into account. This makes the sidereal 
tly more variable than it would be if nutation were 
it the variation, as has just been said, is, after 
all, much smaller than the variations in the rates of the 1 

ver constructed. Since its amount may be cal- 

lever we wish to compare one interval of time 

another as accurately as possible, the uncertainty of 

our measurements of time is in fact nothing more than our 

uncertainty with regard to the uniformity of the Earth s r< 

tion. The true equinox itself is not alwa\ Iy coin- 



272 Outlines of Astronomy. [Sec. 545. 

cident with the point of the equator crossed in March by 
the Sun's centre. 

546. In the course of a single day, the want of strict uni- 
formity in the lapse of sidereal time cannot become percepti- 
ble. We may accordingly assume that the diurnal motion 
(524) of the vernal equinox is perfectly uniform between any 
two of its successive upper culminations. During this inter- 
val, it moves through a whole circle of the celestial spl 

or through an angle of 300°. The sidereal day is divii 
into 24 sidereal hours ; each of these into 60 sidereal 
minutes, and each sidereal minute into 60 sidereal seconds. 
Hence, in one sidereal hour, the vernal equinox moves through 
■fa of the circle, or 15 ; and, consequently, if two terrestrial 
places differ 15 in longitude (526), the local meridian of one 
place will coincide with the meridian of the vernal equinox 
one sidereal hour before the coincidence of the local merid- 
ian of the Other place with the meridian of the vernal equinox. 
In like manner 15' answer to one sidereal minute, and 15 
one sidereal second. 

547. It appears from this that if a clock at each of tw 
restrial places is regulated to such a rate that it will count 
twenty-four hours in one sidereal day. and if the hands of 
each clock are set so as to point, when the vernal equinox 
comes to its upper culmination on the local meridian, to any 
hour which may be agreed upon, the difference of time 
between the clocks answers to the difference of longitude 
between the places. In fact, the difference of time betv. 
the clocks is the angle which their hands would make with 
each other if these hands were put on the same dial ; pro- 
vided that we suppose each clock to have only one hand, 
going round its dial only once in each sidereal day. The 
addition of other hands does not alter the fact that every 
ordinary clock measures time by measuring angles 

clocks and chronometers are considered to be either fast or 
slow, unless the time shown by them when the vernal equinox 
comes to its upper culmination on the local meridian is exactly 
o hours, if the dial-plate shows twenty-four hours, or exactly 



Sec. 547.] Practical Astronomy. 273 

12 hours if the dial-plate is made like that of a common 
3 . that the hour hand goes round it once every twelve 
hours. In using sidereal clocks to determine differences of 
0. we first determine their errors ; that is. we find, 
servations of the stars, how much the time shown by 
ch clock differs from the local sidereal time. We then 
compare the clocks, which may now be done in a lew minutes, 
r tar from each other the clocks may be, provided that 
here they are are connected by telegraph. It is 
.1. after making the comparisons, again to determine the 
error of each clock. In former times, before electric tele- 
hs were invented, it was necessary to carry chronome- 
- backward and forward between the clocks in order to 
compare them ; and as the clocks and chronometers had 
time to change their errors while the comparisons were going 
on, the work had to be repeated many times before satisfac- 
tory results could be reached. There are still other ways of 
comparing clocks ; tor example, the time of the occultation 
:) of a star, or that of the eclipse of a satellite (364). may 
be observed in different places. The difference between the 
clocks, and the error of each clock, being known, we can tell 
what fraction of a sidereal day is required for the passage of 
the vernal equinox from the local meridian of one clock to 
the local meridian of the other. We can turn this fraction 
of a day into a fraction of a circle at the rate of 15 to the 
;r, or we can consider the hours, minutes, and seconds, 
shown by the clock, as angles, instead of considering them 
as intervals of time. Angles of longitude may thus be ex- 
, pressed in time instead of in arc (405). This is the ordinary 
ctice ; and while we are using only sidereal time it cannot 
lead to any confusion ; but since we have mean time also to 
coi reful to know whether we mean an 

in length of time, when k of an h< ur. 

' a minute, or a second. The mean time (311) of one | 
I differs from the mean time of another place by exactl] 

are in the dil 
etwee n the sidereal times of the two places ; for either 
18 



274 Outlines of Astronomy. [Sec. 547. 

of these differences of local time (312) is in fact the angle 
between the planes of the meridians of the two places. But 
a second of mean time is longer than a sidereal second (31 1). 
Right ascensions, the reckoning of which is next to be ex- 
plained, are at the present day almost always stated by means 
of sidereal time. 

548. If the angle between the planes of the meridians pass- 
ing through any two stars is stated in time, the resulting 
number of hours, minutes, and seconds will scarcely differ at 
all (546) from that number of hours, minutes, and seconds 
which denotes the sidereal time during which the local merid- 
ian of any place passes from coincidence with the meridian 
of one star to coincidence with the meridian of the other. If, 
then, we notice the exact sidereal times at which the two 
stars come to their upper culminations on any particular 1 
the difference of these times may be considered as the 
difference of the right ascensions of the stars. But if we 
wish to be precise, we may correct this determination by cal- 
culating the change in the apparent places (514) of the stars 
due to the various movements of the Earth between the 
times of the two culminations which have been observed. In 
practice, when the difference of right ascension between two 
stars is required, the stars must be many times observed at 
their culminations, and each observation corrected for such 
of the Earth's movements as have been learned. When all 
this has been done, any disagreement in the various results 
of the observations may be explained either by mistakes in 
the observations or by unknown movements of the Earth or 
of the stars themselves. If the observations are numerous 
enough, their mistakes will be likely to balance each other; 
so that if any disagreements between the results obtained 
are due to accidental errors, they too will balance each other 
in a particular way which will enable us to distinguish them 
from other disagreements due to unknown movements of the 
Earth and stars. These last disagreements are recorded for 
the purpose of future study of the movements which occasion 
them. In the present state of astronomical research they 
are always very small. 



Sec. 549.] Practical Astronomy. 275 

549. Work of this kind enables us to determine differences 
ension between the stars which we observe But 
us no information about what are called absolute 
right ascensions, or the angles between the plane of the 
meridian of the venial equinox and the planes of the merid- 
ians of particular stars. These must be found by frequent 
observations of the Sun. The time of the culmination of the 
Sun's centre is obtained by observing the culminations of 
both its preceding and following limbs (49), while the zenith 
distances of its northern and southern limbs give us the 
zenith distance of its centre. These observations, like those 
of the stars, must be constantly repeated and corrected. By 
combining them with observations of the stars, we learn the 
Sun's apparent path among the stars. From this we may 
determine the points which we are to regard at any given 
time as the mean and the true vernal equinox, in conformity 
with the plan adopted in our calculations (544, 545). We 
may also determine, from our observations of the Sun's 
course, to what great circle of the celestial sphere the name 
of the ecliptic should be given at any particular time. The 
an^le between the planes of the equator and ecliptic, called 
the obliquity of the ecliptic, varies under the influence of 
nutation as well as in consequence of the fact that the Earth's 
course round the Sun cannot be considered as always lying 
in the same plane, even if the Sun's movements in space 
are disregarded (166). In practice, we calculate the place of 
the ecliptic from that of the equator; so that we may con- 
sider nutation, if we please, as changing the place of the 
ecliptic. When nutation is disregarded, the resulting eclip- 
tic is called the mean ecliptic ; and the angle between its 
plane and that of the equator is the mean obliquity of the 
ecliptic. Having decided on the places of the ecliptic and 
the equinox, we can determine the absolute pi the 

itude and latitude or in right ascension and dec- 
lination. This work cannot be done once for all. but has to 
be continually begun again ; f<<r as not know all the 

movements of the celestial objects, we L.mnot calculate all 



276 Outlines of Astronomy. [Sec. 549. 

their effect beforehand. Still, we can calculate the future 
places of most celestial objects nearly enough to enable 
telescopes to be so pointed, at any particular time in the 
course of many years to come, that the objects may be 
seen through them (no; unless the view is obstructed by 
some opaque body. 

550. The constant repetition of observations made to deter- 
mine the right ascensions and declinations of the stars forms 
perhaps the chief business of astronomical observers. This 
work is monotonous and in itself uninteresting ; it is very 
unlike that looking about for wonderful sights in which most 
people seem to fancy that all astronomers pass their time. 
But the results of the careful measurement of angles of right 
ascension and declination are of great interest and impor- 
tance. They have been the means of making us acquainted 
with the complex precessional movements of the Earth, with 
the distances of several of the stars, and to sonic extent with 
the movement of the Solar System among the stars and the 
general movements of the stars among each other ; although 
our knowledge of these last subjects is as yet scarcely begun. 
Besides all this, the observation of the places of stars is one 
of our means of information with respect to the speed of light 
The movement of light, combined with the movement of the 
Earth in its orbit, alters the apparent place of a star in differ- 
ent ways at different times of year, for reasons which may 
easily be stated. 

551. Every one knows that if he moves forward quickly in 
any direction, when the air is still, there seems to he a slight 
breeze blowing against him. If the air is not still, his move- 
ment will alter the direction with respect to him of any current 
of air through which he may be moving. For instance, if the 
wind is south, and blowing at the rate of ten miles an hour, 
while a traveller moves westward at the same rate, the wind 
appears to him as a south-west wind. If he moves less than 
ten miles an hour, the wind will seem to him more nearly 
south than west ; if he moves more than ten miles an hour, 
it will seem to him more nearly west than south. If the 



551.] Practical Astronomy. 277 

wind is very violent, and the traveller moving slowly, the 
1 will seem to him almost clue south. Still, if he has 
anv way of accurately measuring its direction with respect 
to himself, he may be able to notice that it is a little west of 
south. 

If, instead of keeping on directly westwards, he grad- 
ually turns so as to face the south, the wind will seem more 
and more nearly due south ; and when he is facing exactly 
southwards, his own motion will not change the direction 

n which the wind seems to him to be coming, although 
it will make the wind seem a little stronger than it would 
seem if he stood still. If he continues to turn towards his 
left, he will presently be moving eastwards, and the wind 
will seem to be a little east of south. When he is moving 
exactly northwards, his movement may lessen the apparent 
speed of the wind, but will not alter its apparent direction. 

If the traveller carries with him a straight tube, and 
always keeps it pointed so that the wind may blow directly 
through it, the tube must point due south only when it is 
carried exactly southwards or northwards. If the traveller 
moves at all towards the west, the tube must be pointed 
somewhat west of south ; and if he moves at all towards 
the east, the tube must be pointed somewhat east of south. 
The length of the tube will not make the least difference in 
the direction in which it must be pointed. If the wind ap- 
parently comes from the direction i° west of south, the tube 
must be pointed i° west of south whether its length is six 
inches or six feet. The exact angle which its direction 
makes with the plane of the meridian will depend on the 

• at which the wind blows from the south compared with 
the rate at which the tube is carried westward or eastward. 
554. Now since light is admitted to be a movement of some 
'vement. when combined with the movements of 
the Earth, may be expected to make some slight difference 
in the direction in which any celestial object is seen by a 
terrestrial observer. For instance, if an observer watches 
a star at its upper culmination, he is carried by the Earth's 



278 Outlines of Astronomy. [Sec. 554. 

rotation across the line along which the star's light comes to 
him. Hence, in order to look at the star, he must look a very 
little east of the direction from him in which the star really 
is ; and if he is looking through a telescope along a line in 
the plane of the meridian, the star will seem to pass that line 
a very little later than it would if light moved still faster than 
it does. But the speed of light is so great in comparison with 
that at which a terrestrial place, even one on the equator, is 
carried along by the Earth's rotation, that this change of 
direction, called the diurnal aberration, is too small to be 
accurately observed. It has been calculated from the speed 
which other observations have shown to be that of light. 
From these calculations it appears that a star seems to cul- 
minate about two hundredths of a second later by reason 
of this diurnal aberration than it otherwise would, provided 
it is on the equator, so that its diurnal motion carries it 
daily round a great circle of the celestial sphere, and that 
the observer is on the Faith's equator, where the diurnal 
aberration is greatest. Although the angle of the diurnal 
aberration of one star is the same as that of another, the 
time which the star takes in apparently moving through this 
or any other angle must increase with its declination ; for 
the arc answering to this angle must be measured on a gi 
circle of the celestial sphere, while the circles of diurnal 
motion of all stars not on the equator are small cin l< s of 
the sphere, so that the stars seem to move slower the farther 
they are from the equator (124). 

555. What is commonly meant by the aberration of li^ht 
is clue not to the Earth's rotation, but to its movement in its 
orbit. Its effect in changing the apparent place of a ^tar is 
called annual aberration. The extent of the Earth's orbit 
is near five hundred and eighty millions of miles ; so that as 
there are three hundred and sixty-five days in the year, we are 
carried along by the Earth's movement in its orbit at the rate 
of over one and a half million miles a day, while even if we 
are on the Earth's equator we are only carried some twenty- 
five thousand miles a day by its rotation. Light moves about 



Sec. 555.] Practical Astronomy. 279 

one hundred and ninety thousand miles in a second, so that 
in about eight seconds i: moves as tar as the Earth's move- 
ment in its orbit carries it in a day. Roughly speaking, the 
th's motion in its orbit is always perpendicular to the line 
from the Earth to the Sun ; and this line lies in the plane 
of the ecliptic. Hence it" the geocentric longitude o\ a star 
(532) differs 180° from that of the Sun, the Earth's motion 
in its orbit will carry it directly across the line along which 
the star's light comes to it ; and the star's place will be 
changed as much as aberration can change it, which is of 
course only a little. This greatest angle of aberration, com- 
monly called the constant of aberration, amounts to no more 
than 20". 5. It has not been fully settled whether there is 
any thing in the movement of light by which there may be 
produced an effect like that by which a breeze seems stronger 
when we walk against it (409. 552). 

556. If a star is on the ecliptic, its aberration will merely 
make it seem to move back and forward on the ecliptic over 
an arc of about 41" (20". 5 each way from the middle) in the 
course of a year. In other words, its aberration would be 
only aberration in longitude. But stars which are not on 
the ecliptic will have also some aberration in latitude. For 

mce. if a star is at one of the poles of the ecliptic (531), 
the line along which its light comes to the Earth is always 
perpendicular to the direction in which the Earth is moving; 
for the width of the Earth's orbit is too small to be consid- 
ered in comparison with the distance of any star from the 
rth. Hence a star at the pole of the ecliptic would always 
■m to be 20". 5 out of its place, and would go round that 
• in a small circle in the course of the year. Its aberra- 
1 would be wholly aberration in latitude ; for it would 
always be brought bv aberration towards the ecliptic from the 
e in which it would be seen if the Earth's movement in 
orbit were I. But the change caused by aberration 

m one to another of its apparent places is only a change- 
in longitude. 

557. Any ordinary star has no aberration in latitude and 



280 Outlines of Astronomy. [^ ec - 557- 

most in longitude when its longitude is the same as that of 
the Sun, or differs from the Sun's by 180 , as we have seen. 
It has no aberration in longitude and most in latitude when 
its longitude differs 90 from that of the Sun. But its aber- 
ration in latitude never amounts to the whole of the constant 
of aberration (555), so that its changes of apparent place, 
far as they are due to aberration, carry it round a small 
ellipse, the major axis (145) of which is a line connecting 
the ends of an arc of about 41", while the width of the 
ellipse increases with the star's latitude, but can never 
exceed 41". 

558. From the aberration of any star in longitude and lati- 
tude its aberration in right ascension and declination ma) 
readily calculated. 

559. There is a change in the apparent places of the e 
which, like aberration, is repeated every year in the same 
way. This change is due to parallax (532). It is so small 
that it has been discovered to alter the places of only a 

of the stars, and its amount depends not on the speed of the 
Earth, as aberration does, but on the distance across the 
Earth's orbit. Hence when aberration is greatest, parallax 
is least. If the Earth is directly between a star and the 
Sun, the aberration of the star will amount to the full con- 
stant of aberration, while the star's parallax is nothi 
because its direction from the Sun is the same with its direc- 
tion from the Earth. This enables us to distinguish between 
effects of parallax and effects of aberration. But the largest 
parallax which has been discovered in any star is less than 
1" ; that is, no star is known to change its place as much 
as 2" in the course of the year (1" each way), so far as paral- 
lax is concerned. This shows that the nearest stars are over 
two hundred thousand times as far from the Sun as the Earth 
is (21), unless some stars, the parallax of which has never 
yet been studied, should hereafter be found to be nearer to us 
than those which are now thought to be the nearest. 

560. The movement of a celestial object, combined with 
the fact that its light does not reach us instantaneously, may 



Slc. 560.] Practical Astronomy. 281 

make its apparent place differ from that in which we should 
it it" light moved more quickly than it does. This effect 

>t be taken into account in reckoning the place of a planet, 
and is hence called planetary aberration. It may occur, of 
course, jn the case of a star, but cannot be reckoned, as we 
a little about the distances and movements of stars. 

When all the changes in the apparent places of stars 
which can be attributed to the known motions of the Earth 
have been allowed for, others often remain, as we have seen 

^). That is, after allowing for precession, nutation, 
change of the plane of the ecliptic (166, 167), aberration, 
and parallax, we still find that the right ascensions and decli- 
nations of stars determined at one time do not agree exactly 
with those of the same stars determined at another time some 

: s later. These disagreements are called proper motions 
of the stars in right ascension and in declination. They do 
not always continue with exact uniformity, from year to year, 
but are always small and nearly uniform. We presume them 
to be due to movements of the whole Solar System among 
the stars, and of the stars among each other. So far as any 
thing is yet known of the movements of the Solar System 
among the stars (93), it has been learned by the study of 
proper motions. 

What is called by astronomers the mean place of a 
star for any particular time is its right ascension and decli- 
nation for that time calculated after making allowance for the 
effect of the movement of the mean vernal equinox (545) and 
for the proper motion of the star. The apparent place of the 

r is found from its mean place by adding such small cor- 
rections as may be required. When the apparent place of a 

r is to be calculated for any day, its mean place for the 

Jnning of the year in which the day occurs is first deter- 
mined, and the apparent place found from this mean place. 
In the same way. when the right ascension and declination 
of a: ', its mean place for tin- begin- 

some year is found from this apparent place. All the 
observations of its place belonging to any particular set of 



282 Outlines of Astronomy. [Sec. 562. 

observations have thus to be compared together, in order that 
their accidental mistakes may be made to corre .t each other 
so far as possible (548). 

563. When the movements of bodies belonging to the 
Solar System are observed, the observations can only be 
stated by the use of various terms different from any which 
we have yet noticed. For instance, the nodes of the orbit 
of a planet are the points where that orbit passes through the 
plane of the ecliptic ; or, more usually, these nodes are under- 
stood to be the points on the ecliptic where it is crossed by 
the projection of the planet's orbit on the celestial sphere. 
The ascending node is that at which the planet is observed 
to cross the ecliptic from south to north ; the other is the 
descending node. The line of the nodes is the straight 
line drawn in the plane of the ecliptic from one node to the 
other ( 1 S 1 ). Any great circle of the celestial sphere may be 
considered as having nodes where it - the ecliptic. The 
equinoxes, for instance, may 1 d as the nodes of the 
equator. The equator of the Sun, or of a planet, when re- 
garded as projected on a celestial sphere with its cent! 
that of the Sun or of the planet, is usually described as having 
its ascending node in a certain longitude. 

564. The apsides of an orbit are the ends of its major axis 
(145), or perhaps rather the points where a celestial sphere 
with its centre within the orbit is pierced by the line of this 
major axis, called also the line of the apsides. The peri- 
helion point of the orbit of a planet about the Sun is ob- 
viously at one of the apsides, and the aphelion point at the 
other. 

565. When a conjunction or opposition (327) is regarded 
as taking place at some particular moment, it takes place 
either in right ascension or in longitude, but not usually in 
both at once. A conjunction of two objects in right 
ascension occurs, of course, when both objects have the 
same right ascension. If one is then exactly in a line with 
the other as seen from the Earth's centre they will also be 
in geocentric conjunction in longitude ; as they will, too, 



Sec. 565.] Practical Astronomy. 2S3 

if both of them are on that meridian which passes through 
poles of the ecliptic as well as through those oi the equa- 
tor. This meridian is at once an hour circle and a circle of 
tude; its plane, therefore, must be perpendicular to those 
both oi the equator and of the ecliptic. But when a plane is 
perpendicular to both of two others it is always perpendicular 
to the line of their intersection, it they have one. Hence the 
plane of the meridian passing through the poles of the ecliptic 
is perpendicular to the line of the equinoxes ; and the merid- 
ian itself, which is called the solstitial colure, has the equi- 
noxes for its poles, so that it coincides with the local meridian 
when the equinoxes are on the horizon (536). It crosses the 
ecliptic half-way between the equinoxes, at the points called 
the solstitial points, or the solstices, where the ecliptic 
reaches its greatest declination north and south. If two 
objects, then, are both on the solstitial colure, they are in 
conjunction or opposition both in right ascension and in 
longitude, even if their declinations differ ; while if they are 
on any other meridian, they are in conjunction or opposition 
only in right ascension, and if they are on any other circle of 
latitude they are in conjunction or opposition only in longi- 
tude ; unless the straight line passing through them also 
passes through the centre of the sphere. The calculation 
of eclipses, transits, and occultations is usually begun by 
finding the time of the geocentric conjunction in right ascen- 
sion of the two objects which are to occasion the particular 
event to be predicted. From this, its appearance and time 
for observers on various parts of the Earth's surface may be 
determined, the movement of the two objects in right ascen- 
sion and declination being known. 

the name of solstitial colure is given to the merid- 
ian passing through the solstices, that which passes through 
the equinoxes is called the equinoctial colure. 

ution from one conjunction with the Sun to 
the next conjunction of the same kind is called a synodical 
revolution, as we have seen (335) ; and the- times of the 
synodical revolutions of the Moon and Venus, for example, 



284 Outlines of Astronomy. . 567. 

are more easily noticed than those of the sidereal revolutions. 
A sidereal revolution is the revolution of any object from its 
passage through some given plane, perpendicular to the plane 
of its orbit and containing one focus of that orbit, to its next 
passage but one through the same plane (335). Practically, 
however, a sidereal -evolution is completed by the return 
of any object to conjunction in longitude with EJiy star so 
distant that its proper motion (561) is imperceptible; the 
centre of the sphere being placed at one focus of the orbit 
of the revolving object. A sidereal revolution is actually 
reckoned by making a correction in the time of some other 
revolution so as to allow for the theoretical movement of the 
point from which that revolution is reckoned. 

56S. The true anomaly of a planet, at a given moment, is 
the angle through which its radius vector (148) has moved 
since the planet's last perihelion p lis mean anom- 

aly, at a given moment, is the angle through which its radius 
vector would then have moved since the planet's last peri- 
helion passage, if the radius vector moved over equal angles 
(instead of equal areas) in equ il times, at a rate sufficient to 
bring it to the perihelion point at the actual time of each 
perihelion passage of the planet. 1 Ienre the mean anomaly 
is less than the true anomaly between perihelion and aphe- 
lion, greater than the true anomaly between aphelion and 
perihelion, and differs most from the true anomaly at those 
times when both anomalies are increasing at the same rate. 
What has been said of the Moon's movements (177) may help 
to make this clearly understood. The anomalistic revolu- 
tion of any object moving in an orbit around another is its 
revolution from a point after passing which its distance from 
the body round which it moves begins to increase to the next 
point at which this happens. For example, the anomal 
revolution of the Earth, the time occupied by which is the 
anomalistic year, is the revolution of the Earth from peri- 
helion to perihelion ; the anomalistic revolution of the Moon 
is its movement from perigee to perigee again (335). 

569. Still another kind of revolution is revolution from one 



Sec. 569.] Practical Astronomy. 285 

of the nodes of an orbit round to the same node ; this is some- 
times called nodical i evolution. 

570. The sidereal, anomalistic, and nodical revolutions of 
any large planet belonging to the Solar System differ little 
from each other. The nodical revolution is usually the 
easiest of the three to determine by observation, since when- 
ever a planet appears to cross the ecliptic, it must be at one 
of its nodes; while the Earth, from which it is observed, 

s not remain in any place from which the times of the 
sidereal and anomalistic revolutions of the planet can be 
readily determined. 

571. But since orbits have to be regarded as continually, 
though slowly, changing their planes, and their places in 
those planes, it is obvious that neither the nodical nor the 
anomalistic revolution of a planet can precisely agree with 
its sidereal revolution, which, as has been said, is that usually 
meant when the revolution of a planet is spoken of (335). 

572. Although these small distinctions between different 
sorts of revolution may seem needless, they all have their 
uses in astronomical research. What has already been said 
of the movements of the Earth and of the Moon, will show 
that the different revolutions of these bodies, especially those 
of the Moon, perceptibly disagree in the times which they 
occupy. We have seen that the nodes of the Moon's orbit 
retrograde so rapidly as to make the complete circuit of the 
ecliptic once in something less than twenty years (181) ; 
hence the nodical revolution of the Moon must be shorter 
than its sidereal revolution ; for the nodes of its orbit back 
round to meet it while it is going round the Earth. Again, 

les of the Moon's orbit turns round with 
direct motion (1S4) once in about nine years, so that the 
Moon's anomalistic revolution is longer than its sideia 1, 
though not so long as d revolution: for the line 

trth to the Sun turns round with direct motion 
id of once in nine 1 that the Moon'8 

conjunction is than its return to perigi 

573. The Earth has no nodical revolution, sin< e the pi, me 



286 Outlines of Astronomy. [Sec. 573. 

of its orbit is not regarded as differing from the plane of the 
ecliptic. But the most important of its revolutions, so far 
as the ordinary reasons for dividing time into years are con- 
cerned, is its revolution from either equinox to the same 
equinox again. This is called the tropical year ; it contains 
a little less than 365^ days of mean time, and hence a little I 
than 366J- days of sidereal time. As the year, however, must 
have an exact number of days in it to make it convenient for 
common purposes, our ordinary year, called the civil yeai 
one of 365 days of mean time. Every fourth year contains 
366 days, so as to prevent the civil and tropical years from 
disagreeing too much as time goes on. But as the tropical 
year is not quite 365* days, the additional day usually put 
into the civil year once in four years is left out every hundred 
years. The year 1800, for instance, had 3^5 days, and the 
year 1900 will have no more, lint every 400 years the day 
must be added to the civil year as usual. The year 2000 
will have 366 days, or, according to the usual expression, will 
be a leap year. Further corrections, at long intervals, may 
be made in like manner. The reason why the civil \ 
begins a little after the winter solstice has already been men- 
tioned (302). 

574. The seasons, and all the events connected with them, 
depend on the tropical year; except in the study of astron- 
omy, then, it is the only year which is noticed But the 
sidereal revolution of the Earth takes a few seconds more 
than its tropical revolution ; for the equinox ^.rade on 
the ecliptic like the nodes of the Moon's orbit, though much 
more slowly (167, 544). So, too, the apsides advance (169) ; 
and accordingly the anomalistic year (568) is very slightly 
longer than the sidereal year. There is no synoclical year, 
since we count years only by the apparent movements of a 
single body, the Sun ; but if we please, we may consider the 
time of the synodical revolution of any planet as the synodi- 
cal year of the Earth with respect to that planet. 

575. Any one of the moments at which the mean time clock 
is to agree with the sundial in the course of a year may be 



Sec. 575.] Practical Astronomy. 2S7 

chosen at pleasure, as we have seen (310). The choice is 
ually made in the following manner. For convenience in 
laining it. it is usual to suppose an object called the mean 
sun, having a uniform direct motion along the equator, and 
ising the vernal equinox once in each tropica] year. The 
question now to be decided is this : at what time in the trop- 
ical year is this mean sun to pass the vernal equinox? The 
moment chosen for this purpose is not that when the Sun 
lally crosses the equator from south to north, but that at 
ich it would cross the equator, if, after the time when the 
Earth passes its perihelion, it moved along the ecliptic at the 
of the mean sun's movement along the equator. In other 
words, since the Earth passes its perihelion early in Januarv, 
the moment chosen for the passage of the mean sun through 
the vernal equinox is the first moment after the Earth's peri- 
helion passage at which its mean anomaly (568) is equal to 
the angle between the line of the apsides of its orbit and 
the line of the equinoxes. At this moment, the Earth's true 
anomaly exceeds its mean anomaly ; hence the Sun is already 
north of the equator, in advance of the mean sun in its direct 
movement, and therefore behind it in its diurnal movement, 
so that the sundial, as we have seen (310), is slow of the 
mean time clock. By reckoning backward or forward from 
this moment, we can find the times of the four yearly con- 
junctions in right ascension of the mean sun with the Sun, 
which are obviously the times when the mean time clock 
should agree with the sundial. 

It is clear that the difference of local mean time be- 
tween two local meridians is the same with their difference 
of 1 real time ; for the mean sun passes from one 

meridian to the other in a fraction of twenty-four hours of 
mean time, equal to the fraction of twenty-four hours of side- 
time in which the vernal equino; 3 from one merid- 
ian to the other. That is. when v. illy speaking of 
the differ meridians, which 
_le, it makes 1 ,Je is meas- 
ured on the dial of (me clock or ier (547J. 



288 Outlines of Astronomy. [Sec. 577. 

577. In reckoning mean time, the mean equinox (545) is 
employed ; so that clays of mean time are still more nearly 
equal to each other than sidereal days are. A perfectly uni- 
form measure of time might be obtained (supposing the 
Earth's rotation to be uniform; by assigning a uniform re 
grade movement to the equinox, and separating time into 
parts by means of the successive returns of the mean sun to 
this uniformly moving equinox. This plan has been pro- 
posed, and the time so measured has been called equinoctial 
time. It would be alike at all parts of the Earth (312). 
But astronomers have generally contented themselves with 
avoiding the use of local time, in certain calculations. 
the following means. Adding together, at any given time, 
the heliocentric longitude of the Earth's perihelion, and the 
Earth's mean anomaly, we obtain an angle called the Earth's 
mean longitude. What is (died the Sun's mean longi- 
tude differs from the Earth's by l8o°. Now the astronomi- 
cal year (or, as it is sometimes called, the fictitious v 
is considered to begin at the moment when the Sun 
longitude is 280 . The time called 1S75.0, for instano 
the moment nearest to the beginning of the civil \ 
when the Sun's mean longitude is 2S0 ; and the time c 
1875.5 is half a tropical year after 1S75.0. The tropi 
since it is reckoned from the mean equinox, is ai 
invariable as the day of mean time ; when a still less variable 
measure of time is wanted, it may be specially calculated for 
the occasion on which it is required. The actual tropical 
year, comprised between two passages of the Sun from the 
southern to the northern side of the plane of the equ itor. is 
more variable than the tropical year just described, but r 
greatly differs from it. 



57S.] Astronomical Instruments. 2S9 



CHAPTER XIII. 

ASTRONOMICAL INSTRUMENTS. 

A sundial is made by setting up something with a 

tight edge so that the shadow of this edge may fall on a 

surface where the hours of the day may be marked. What- 

r is set up for this purpose is called a gnomon. The 

xe of the gnomon by which the shadow is to be cast must 

as nearly as may be parallel to the Earth's axis. If the 

declination of the Sun always remained the same, this would 

be necessary. Suppose the plane of any great circle of 

re to contain the cd^c of the gnomon by which the 

low is cast. Then suppose a point of the Sun, at some 

particular moment, to be also in the plane of this circle. As 

3 as it remains there, the gnomon must cast a shadow in 

plane of the same circle. But if the luminous point 

which occasions the shadow changes its declination without 

moving in right ascension it will be carried out of the plane 

which passes through the edge of the gnomon and the 

original place of its shadow, unless this plane is that of a 

meridian. Hence, if the shadow did not lie at first in the 

plane of a meridian its place on the dial must be changed 

by any movement of the Sun in declination alone. , Now as 

the Sun his different declinations at the moments on almost 

any two days when it is crossing any given local meridian, 

the shadow of a gnomon will not daily fail along the same 

line when the Sun crosses a given local meridian, unless the 

is in the plane of that meridian. Strictly 

: the gnomon cannot be at once in the 

planes of all local meridians, without forming part of the axis 

the Earth, lint th< of parallax pro iov- 

the centre of the celestial sphere from the Earth's centre 

nt on its surf 3 not noticeably alter the 

19 



290 Outlines of Astronomy. [Sec. 578. 

apparent place of the Sun. Hence, if the edge of the gno- 
mon is parallel with the Earths axis, and its shadow falls 
along a certain line on the dial when the Sun is crossing 
given local meridian, it will fall along the same line on any 
other day at the time when the Sun crosses that meridian. 
If the edge of the gnomon is in a plane parallel to that of 
any local meridian, its shadow will always fall along a cer- 
tain line when the Sun crosses that meridian. Thus, if the 
edge of the gnomon is in the vertical line, or in any other 
line which lies in the plane of the meridian of its own pla 
it will cast a shadow due north when the Sun culminates. 
The shadow of any thing which is upright will accordin 
serve to show when it is noon by the Sun, if the lin< 
known along which the shadow lay at noon by the clock on 
one of those days in the year when the clock and sum 
should nearly agree. In the same way the north and south 
points of the hori/on can he roughly determined. If the dial 
on which the shadow of the edge of the gnomon falls is part 
of the surface of a sphere having the edge of the gnomon for 
one of its diameters, the hours may he marked upon the dial 
at equal intervals ; hut if, as is customary, the dial is flat, 
the spaces between the hour-marks must differ in width. 

579. Time-pieces which are to keep mean or sidereal time, 
and not apparent time (317,), are made by giving a turning 
motion to wheel-work either by a weight or a spring, and 
keeping the motion as uniform as possible by means either 
of a pendulum or of a spring. If the pendulum is used, the 
time-piece is usually called a clock, whether it is driven by 
a weight, a spring, or by any other contrivance ; but if its 
motion is regulated by a spring, it is called a chronometer 
if it is large, and a watch if it is small. It would be impos- 
sible to describe the construction of clocks and chronome- 
ters within reasonable limits in a small work like tl. 
moreover, so far as their astronomical uses are concerned, 
we need only know that they are meant to run at some uni- 
form rate, but that in practice it is impossible as yet to make 
them do so. Hence, in using any time-piece, we must fre- 



Sec. 579.] Astronomical Instruments. 291 

quently determine its error, in a manner presently to be 

ined. 
Various applications of electricity have been con- 
trived for the purpose of registering time. The facts of 
electrical action must be learned from those treatises the 
object of which is to explain them ; but it may be well here 
to describe one of the ordinary forms of the chronograph, 
an instrument by which many astronomical observations are 
now recorded. 

The wheels of this kind of chronograph, like those 
of a clock, are put in motion by a weight, and their motion 
is regulated by a pendulum ; but instead of turning hands 
upon a dial, they turn a rather short and wide tube of metal 
set at each end of this tube, which is called the 
barrel of the chronograph. A piece of paper is wrapped 
round this barrel, and a pen is fixed in a frame which slowly 
mov from one end of the barrel to the other. The 

k-work is regulated so that the barrel may turn round 
a uniform motion, once in every sidereal minute. Ac- 
lingly, if the pen is made to rest on the paper, it draws 
a line upon it which goes spirally round and round the bar- 
rel the length of every turn of the spiral representing one 
minute of sidereal time. In the frame which carries the pen 
is an electro-magnet and a spring. When the magnet stops 
acting, the spring pulls the pen a little nearer to the end of 
the tube from which the motion of the frame is carrying it ; 
and when the magnet begins to act again, it pulls the pen 
back to its place. The magnet is made to act by an electric 
current, and any clock which is to be used in the observa- 
s for which the chronograph is wanted stops this current, 
tit at a time, at regular intervals of one or two 
seconds. It to construct the clock so that it will do 

Marks are thus made along the line drawn by the pen, 
whi' the moments at which the clock stopped the 

*ric current. The clock is made to omit one of its - 
in every minute, so as to show when the minute began. 
: the minute shown by the clock when it begins to 



292 Outlines of Astronomy. [Sec. 581. 

record its seconds upon the chronograph is noted, the time, 
according to the clock, of any second recorded on the chron- 
ograph can be ascertained after the paper is removed from 
the barrel. The observer is provided with means of stop- 
ping and restoring the electric current whenever he pie; 1 
Hence he can make marks upon the chronograph of a some- 
what different form from those made by the clock. When 
he wishes to record the time of an observation, he makes 
one of these marks at the moment when he notices the event 
the time of which is wanted. This mark will appear among 
the marks made by the clock, the times of which are known, 
as explained above : and the time when the observer's mark 
was made can therefore be ascertained 

582. Since electric signals may be exchanged between any 
two places which can be connected by telegraphic wires, the 
time of an astronomical observation maybe recorded 1 
chronograph at a great distance from the place where the 
observation is made. The culmination of a star at San 
Francisco, for instance, maybe recorded by a chronograph 
in New York : and in like manner the clocks of th 

cities may be compared with each other (54;). Even with- 
out using a chronograph, we may put a clock in connection 
with a telegraphic wire in such a manner that it will send 
signals along the wire at regular intervals. By this me 
a clock kept at an astronomical observatory is often made 
send signals to different places in the country around it 
that the clocks kept at those places may be compared with 
it at any time. The running of these clocks is sometimes 
actually governed by electric apparatus, so that their p 
dulums all swing at the same rnte as that of the pendulum 
in the clock by which the electric currents arc interrupted. 

583. When an angle can be measured by an interval of 
time (510, 548), a good clock or chronometer is the only 
instrument needed for its measurement. But most angles 
cannot thus be measured ; and angles which cannot be meas- 
ured by a clock are generally expressed only in arc. and never 
in time (405). They are measured on graduated circles, or 



Sec. 5S3.] Astronomical Instruments. 293 

luated arcs of circles, when the measurements need not 
be very precise ; if great accuracy is required, the measure- 
its are wholly made, or at least completed, by instruments 
called micrometers. 

Graduated circles are usually made of metal, some- 
it in the shape of ordinary wheels, so as to be light, 
and stiff; for if they bend, their usefulness is much 
>ened, and if they are needlessly heavy, their own weight 
may bend them a little. Their graduations, or, in other words, 
the marks made upon them for the measurement of angles, 
are usually placed near their limbs : this word being applied 
to instruments in a sense like that in which it is applied to 
the disks of celestial objects (49. 183). The graduation of a 
circle often shows a mark for every tenth minute of arc : that 
marks round the edge of the circle, as nearly 
at equal distances from each other as they can be made. 
Sometimes circles are graduated to every fifth minute of arc, 
so that the graduation consists of 4320 marks ; 360 of the 
marks, at equal distances from each other, are made longer 
than the rest, so that they may serve in reckoning degrees. 
One of them is taken for the point from which measurements 
on the circle are to begin, and numbers are engraved beside 
the graduation at places enough to show what number of 
decrees and minutes is contained in the arc between any two 
lines. When none of the angles to be measured are very 
larcre. a graduated arc will answer instead of a whole circle : 
but when ^reat accuracy is wanted, it is best to use a whole 
circle, and to measure any required angle upon several differ- 
ent parts of it. 

en if the graduation is carried to every fifth minute 

of arc. it is not sufficient for the accurate measurement of 

*les. We mav want to know the anc^le between the begin- 

aation and some point on the limb of the 

en two of the marks. In many cases of this 

I, we can obtain a sufficiently accurate measurement by 

vernier. A vernier i^ a gradu rks 

on which are equally distant from each other, but either 



294 Outlines of Astronomy. [Sec. 585. 

farther apart or closer together than those of the gradua- 
tion with which it is meant to be used. Suppose that a 
circle is graduated to every tenth minute of arc, and has a 
vernier beside it, ten divisions of which take up as much 
space as eleven divisions of the circle. Then, since the arc 
between two neighboring divisions of the circle is io', the 
arc which eleven divisions take in is no'. Ten divisions of 
the vernier take in this same arc. and the arc between any 
two neighboring divisions upon it is therefore n'. The ver- 
nier is set so that one of its marks is exactly opposite the point 
on the circle to which we wish to. measure, and the mark on 
it which is most nearly opposite one of the marks on the 
circle is then looked for. If this mark is four divisions away 
from the point to which we are measuring, this point is 44/ 
from the mark on the circle most nearly opposite a mark on 
the vernier, and therefore 4' from the nearest mark to it 
the graduation of the circle. With this vernier we can ac- 
cordingly measure an angle upon our circle correctly within 
i'. A vernier with a different graduation might enable US 
measure arcs of 10" or even less. Verniers are in common use 
for measurements of small distances as well 

586. But astronomical measurements must often be made 
more accurately than they can be made by means of verni 
We must then resort to micrometers. These are usually 
small frames pushed or pulled one way or the other by the 
turning of screws. The number of turns, or fractions of a 
turn, given to the screw of a micrometer, shows how far its 
frame has been moved. The micrometer, then, measures 
distances, not angles, since the movement of the frame is 
rectilinear, as nearly as may be. It is not adapted, therefore, 
to the measurement of large angles ; but the angles measured 
by micrometers are always so small that they may be com- 
pared with each other without any error of importance by the 
comparison of the lengths of straight lines drawn across them 
from one side to the other. Moreover, the error, if there is 
any, may be calculated and allowed for. 

587. Micrometer frames are usually set within the tubes 



Sec. 587,] Astronomical Instruments. 295 

of telescopes, at the places where [mages are formed of the 
jects which are to be measured (483)1 The frames carry 
spider's threads or delicate lines of some kind, which are 
brought opposite the points to which the measurements are 
made. When a micrometer is used, instead of a vernier, to 
read a graduated circle with accuracy, it is put into a micro- 
scope, which is made like a small telescope, with an object- 
glass and eye-piece ; but as it is used for looking at near 
objects, the place in the tube where the images are formed, 
and where the micrometer is set, is farther from the object- 
glass than it would be if distant objects were to be observed 
with the same instrument. The movable thread may be set 
first on a fixed mark in the microscope, and then on the 
nearest division of the circle as seen through the micro- 
scope : and the exact setting of the microscope with re- 
spect to the circle, which is generally the thing to be 
determined, may thus be measured. There are various 
contrivances for shortening this process in practice. Angles 
may be measured with micrometers to the fraction of a 
second of arc. 

The name of micrometer is given to other instruments 

des the frames moved by screws which have been men- 
tioned. A ring micrometer, for instance, is a flat metal 
ring set in a telescope. The different times which are re- 
quired for the passage of objects, by reason of their diurnal 
movement (5241. across the ring at different distances from 

centre, enable us to calculate the angles between the 
objects. 

Telescopes and measuring apparatus are used to- 
gether by astronomers in a variety of ways, only a few of 
which need here be noticed. The sextant, quadrant, or 
reflecting circle, all of which are different forms of what 
D principle a single instrument, will first be described. It 

t not be confounded with the large sextants and quad- 
rants used for measuring angles by early astronomers. The 
modern sextant is the most portable of all astronomic. d 
instruments, and does not need a steady foundation to rest 



296 Outlines of Astronomy. [Sec. 589. 

on; for which reason it is the only instrument with which 
astronomical observations can be made at sea. It is used to 
measure the arc between two objects on the great circle 
of the celestial sphere which passes through them. A 
small telescope is pointed at one of the objects, while a 
movable mirror is turned until the light which it receives 
from the other object is thrown upon a second mirror and 
thence upon the object-glass of the telescope, so that both 
objects are seen at once, and may be brought to apparent 
contact. The angle between them is determined from the 
angle through which the movable mirror has been turned to 
produce the required effect. The altitude of an object may 
be measured in like manner, the point of the horizon neai 
to it being taken for the second object. From the altitude of 
the Sun observed at noon, the latitude of the place of no- 
vation may be calculated; and observations of the Sun's 
altitude at Other times of day enable the local time to be 
determined when the latitude is known. Sir rally 

carry chronometers set to the local time of Greenwicl 
some other place on land; and on air ion when the 

local time of a ship has been determined, it may be com- 
pared with that of the chronometers on board, with the object 
of finding the difference of longitude between the ship and 
the meridian the local time of which is kept by the chro- 
nometers (547, 576). 

590. The second mirror of a sextant, by which the reflected 
light is thrown into the observing telescope, must be pla< 

of course, partly before the object-glass ; but it > as 

not entirely to cut off the direct view of distant objects 
through the telescope which is required in using the in- 
strument. The sextant is little used at sea except in 
observations of the Sun's altitude ; but it is occasionally 
useful in observations of the Moon and stars, both at 
and on land. 

591. The transit instrument, in its ordinary form, consists 
of a telescope mounted on an axis which is intended to be as 
nearly perpendicular as may be to the line of sight (4S6) 



Sec. 591.] Astronomical Instruments. 297 

through the telescope, and also to be as nearly horizontal 
ssible, so that the line of sight, when the telescope is 

turned round, may always remain in the plane of some one 

;ical circle. This can never be perfectly accomplished ; 

but the more nearly it is done, the less calculation is needed 

the required results from the observations made with 

the instrument. These observations consist in recording the 

times according to some clock or chronometer at which stars 

are carried by their diurnal motion across marks set in the 

Id (483, 487) of the telescope. 

In order to determine the error of a clock, or the 

longitude 1547) of a terrestrial place, a transit instrument is 

usually placed so that its line of sight may be as nearly as 

ssible in the plane of a local meridian; it is then said to 

be in the plane of the meridian. Sometimes, however, it is 

>me vertical plane other than that of a local meridian, 

ecially in the plane of some vertical circle which the star 

Polaris may be about crossing at the time of the observations. 

Observations for terrestrial latitudes are sometimes made 

th a transit instrument in the plane of the prime vertical 

593. When a carefully graduated circle is set on the axis 

of a transit instrument, the whole instrument takes the name 

. transit circle, or meridian circle ; for an instrument of 

this kind is always set as nearly as may be in the plane of 

the meridian, and used mainly for the purpose of determining 

the right ascensions and declinations of celestial objects. The 

luated circle is usually fastened upon the same axis with 

the telescope, and turns round with it : in this case, the 

microscopes and micrometers used for measurements on the 

re set on the solid piers which support the whole 

•rument. so that one part after another of the limb of the 

cir fore them as it turns. If then, the 

lin< »ugh the telescope is pointed towards a 

3 the meridian, the angles between the beginning 

the graduation of the circle and the points in it lying in 

the lines of sight through the micro termined 



298 Outlines of Astronomy. [Sec. 593. 

by the graduation and the micrometers. If a like observation 
is afterwards made on another star as it crosses the meridian, 
the differences between the angles thus obtained and th 
previously recorded will show the difference of declination 
between the stars. As the line of sight through the ti 
cannot be accurately pointed to any star, a micrometer of 
some kind in Ihe telescope itself is used to measure the 
angles between the line of sight and the lines pointing to 
the stars. 

504. Differences of right ascension are deduced from a 
Comparison of the recorded times of the ; 
Over the lines in the field of th id if 

absolute right ascensions the Sun 

must be observed. Then rious ways of determii 

the angles between the beginning of the graduation on the 
circle in any given position and the points on it thro 
which a line parallel with the Earth's axis won' 
these angles being needed when not merely tin 
of declination between different stars, but their declinations 
themselves, are required 

595. Altitude and azimuth instruments, in addition to 
the vertical graduated circles of meridian instruments, have 
horizontal graduated circles, and can be turned round on a 
vertical as well as on a horizontal axis. Instruments of this 
kind are seldom used for astronomical pui 

when made on a small scale, they are in much use am 
surveyors, under the name of theodolites. But the instru- 
ments called zenith telescopes and vertical circles, which are 
of use in astronomy, are in fact modifications of altitude and 
azimuth instruments. They are chiefly used for the deter- 
mination of declinations and of terrestrial latitudes. 

596. A telescope is said to be equatorially mounted, or is 
called an equatorial, when the frame which carries it maybe 
turned upon either of two axes perpendicular to each other, 
one of which, called the polar axis, is meant to be parallel to 
the axis of the Earth : the other is called the declination 
axis. The chief object of this mounting is to enable the 



THE GREAT TELESC 

a.SJTavaLObsenratcB 

Plate XI I L 




This figure is copied from a photograph taken at Washington. The 
focal length of the telescope is about thirty feet, and its aperture twenty- 
six inches. It is nounted equatorially. The instrument is here repre- 
sented nearly in the plane of the meridian, so that the declination axis 
is nearly horizontal. 



596.] ASTRONOMICAL INSTRUMENTS. 299 

follow the diurnal motion of a star by simply 
the telescope on its polar axis as fast as may be 
this can be clone by clock-work, so that a star 
. be kept in the field and observed lor a considerable 
time without the need of any movement of the telescope by 
server. Equatorials, therefore, are the only instru- 
>ui table for observations which require much time ; 
but they cannot be supported as steadily as meridian instru- 
and are consequently unsuited to the determination 
I>ut when two objects are nearly enough in 
e direction from the observer to allow them both to 
be seen at once in the field of an equatorial, or both to be 
rved within a few minutes' time and with little move- 
nt of the instrument, their differences of right ascension 
declination may be accurately determined with an equa- 
torial provided with a suitable micrometer (5S6, 58S). Thus 
the place of an object which is in sight only for a short time. 
f a faint object, with reference to a star seemingly near 
and with an equatorial, and the right ascension 
and declination of the star afterwards determined by a merid- 
ian circle. 

rtroscopes and photographic apparatus when used 
in astronomical researches, are generally attached to equa- 
ds : and equatorials are likewise employed for observa- 
tions of double stars, and of parallax (SS'l)'- the parallax of 
rs being usually determined by the micrometric comparison 
of their places with those of other stars too remote to hive 
a noticeable parallax. The largest telescopes are usually 
mounted equatorially. 

Instruments intended for precise observations must 
e firmly mounted on foundations separate from those 
*'ie building in which they are placed, and must be pi 
tected. so far a- possible, from accidental jarrin^ 

' even from sudden changes of temperature. 
are in actual use. the rooms in which they stand must be no 

if it can 
the bail r the currents of air which would 



300 Outlines of Astronomy. [Sec. 598. 

sioned by neglect of this rule would make the images of the 
objects observed very unsteady. But after all possible care 
has been taken to make observations correct, the d\ 
the instruments employed in making them will render them 
to some extent erroneous. For example, the line 
through a meridian circle can neither be kept long in the 
plane of a meridian, nor even perpendicular to tl f the 

instrument. Hence arises the necessity of many calculati 
by means of which these instrumental errors may be ascer- 
tained and allowed for in obtaining the results to be derived 
from the observation* n when t 1 >ns have 

been freed from tl tof instrumental error, the remain- 

ing portions of their reduction, as the work of calculal 
their results is called, usually require much la -tro- 

nomical ol»i I themsel e rally b\ 

the smallest part of the work of astronomers. It would be 
useless to attempt the explanation of the methods by which 
the results of modern astronomy are actually reached to 
sons not familiar with mathematics ; but in the short account 
of the progress of astronomical knowledge hei to be 

given, we shall have occasion to notice the general 1 
observation and reasoning which has led to the conclusions 
accepted by modi 



599-] Theoretical Astronomy. 30* 



CHAPTER XIV. 

THEORETICAL ASTRONOMY. 

599. Whatever the actual path of a moving material 
object may be, we always regard the object, at any particular 

mt, as moving in some particular direction and at some 
particular rate. In fact, without making this supposition, we 
should not know how to set about studying the movements 
of material objects at all. It is clearly not always a correct 
supposition ; and we do not know that it is ever correct, for 
we cannot tell any thing about the actual paths of moving 
objects (112). But we find it answers the purpose of help- 

us to draw up the rules, or laws of nature, by which we 
can tell pretty accurately what to expect with regard to move- 
ments not yet completed (117) ; just as we find it practically 
useful to regard a moving object as first occupying one place 
and then another, without troubling ourselves with the puzzle 
it is that this object gets from the first place to the 
second (393). 

600. When we have occasion to consider the way in which 
any law of nature works in a particular case to which it ap- 
plies, and at a particular instant, we often find it convenient 
to say that a force is acting at that instant according to that 
law. When the law is a law of motion, the force is a motor 
force ; but as we shall have no need of considering any but 
motor forces, we may call them simply forces. The use of 

word force is explained by the following statement, gen- 

ly called a law of motion, but in fact rather an account 

of the sense to be attributed, in the study of physical science, 

tions made with respect to motor forces. Forces act 

. nut arc proportio)iaI to the velocities tiny 

fuce This amounts to saying, first, th.it at any parti cu- 

lar instant every material object to which any law of motion 



302 OUTUN MY. 600. 

is applicable must be regarded as moving in some particular 
direction at the rate required by that law ; but since one 
law may be applied in different ways to the same < 
prevents confusion between these different applications 

describe the tacts for which they account as different 

forces. When we resolve (115) the motion of an object at a 
particular instant, and in a particular direction, into a num- 
ber of motions, each in some particular direction of its own, 
we say, secondly, that the force moving the object in on< 
these di r ec t io n s, as compared with tint moving it in ano; 
is greal in proportion to the rate of its movement in the '. 
direction as compared with the r.ite of its movement in 
other. Thus, if only two applications of one law, <»r of 
different laws, of motion are made at oik ular 

object, and the object is consequently 

twice as fast, for example, in one direction as in another, it 
is said to be moved by tW< one twh 1 

other. This use of language obvious' 
and therefore much labor which would otherwise be S] 

in considering their meaning. Th< I the 

word force may be compared to the use of letters of the alpha- 
bet in algebra. We need not know just what these lett 
Signify, so Long as we understand that each letter never 
changes its signification during any particular course of 
reasoning in which it is empfoj 

601. One of the laws of motion can only be applied in one 
way at once to any particular object ; and hence there is 
little need of using the word force in describing its applica- 
tions. This law is that every body continues in its state of 
Test or of uniform rectilinear motion. >' as 

Other laws of motion may be applicable to it. That is. if a 
body begins to move, there must have been a change in it^ 
circumstances, owing to which it is set in motion : and if it 
is once in motion, there must be some change in its circum- 
stances either to stop it, to change the direction of its motion, 
or to change the rate of that motion. When a force is con- 
sidered as acting under this law, it is called the force of 



Sec. 6oi.] Theoretical Astronomy. 303 

inertia, or simply inertia ; and the law may be called the 
law of inertia. Headway, in common language, sometimes 
is inertia, as well as the movement due to inertia. 
. Another law of motion is usually expressed bv say- 
that action and reaction arc equal and opposite. Suppose 
that a ship is towed by a steam tug at the rate of four miles 
an hour, and that the tug could go ten miles an hour without 
putting on any more steam, if it did not have to tow the ship. 
Wo then resolve the motion of the tug into two ; one motion 
forwards at the rate of ten miles an hour, and another back- 

rds at the rate of six miles an hour. In order to explain 
the movements of the tug and of the ship as fully as possible, 
we should have to take account of a great number of laws of 
nature ; but our present purpose makes it convenient for us, 

ead of stating these laws, to consider all their effects 
together under the name of two equal forces ; one force by 
which the tug pulls the ship forward four miles an hour, and 
another force by which the ship pulls the tug backward six 
miles an hour. These forces are obviously opposite, and are 
to be considered equal. The law that action and reaction 
are equal and opposite requires us to suppose a reaction 
equal and opposite to every action whatever. 
603. It may seem incorrect, in the example just given, to 
that the forces by which the two vessels pull each other 
are equal forces ; for, as we have seen, forces are propor- 
tional to the velocities they produce, and yet we have re- 
garded the ship as pulling the tug backward half as fast again 

the tug pulls the ship forward. But it has been explained 
that we compare forces merely by comparing the rates of 
the different movements of some one thing ; if we compare 
the rate of movement of one thing with that of another, we 
cannot call this a comparison of forces without using the 

rd force in two different ways in a single course of reason- 
ing (600). 

604 Every thing which we can observe differs more or 
less from every thing else, so that in studying it we have to 
make rules which apply to it alone. However, these rules 



304 Outlines of Astronomy. [Sec. 604. 

can often be drawn up by the help of others which are more 
general. The rule that action and reaction are equal and 
opposite is an instance of a general rule of this kind. By its 
help, in the case just given, we find an effect of certain 
iarities about the ship, which we may call the amount of 
work done in pulling that ship at the rate of four miles an 
hour. We feel sure, after trying this experiment, that i 
other tug, built exactly like the first, can pull the same ship 
four miles an hour, and is then set to pulling against the fir.^t 
tug, neither tug will pull the other from its place. But with- 
out the rule that action and reaction are equal and op| 
we could not be sure that the action of the second tug would 
be equal to that of the first ; since one or both of these actions 
might have been unequal to the reaction of the shi] 
course, in f this kind, we take the rule for granted, 

and are not obliged to think of it at all; but it should he 
remembered in the study of the movements « 
objects. 

605. The chief differences among the objects which we 
shall have to consider are differences of mass. W< 
seen 1 10) that we get our first notion of mass by n< 
that bodies which differ in size, but not in hard: 
or general appearance, differ in certain other ways in just 
that proportion in which they differ in size. A quart of 
water, for instance, is just twice as large, and also just 
as heavy as a pint of water ; and just enough quicksih 
outweigh a quart of water takes up twice as much ro 
the quantity of quicksilver which will just outweigh a pint oi 
water. But however the notion of mass is gained, tin 
is used in astronomy to mean merely those properties 03 
any celestial object, except its shape, which make 
rule necessary for its movements and for the movements 01 
other objects with respect to it (604). When we say that thf 
mass of one object is three times t as that of another 

Ave mean that a movement of the first object must 
ered three times as great as a movement of the second objeo: 
through the same distance ; or that the two objects differ in 



Sec. 605.] Theoretical Astronomy. 305 

h a way that a movement of the first object through one 

A will balance a movement of the second object through 

. ird, under the rule that action and reaction are equal 

te. The amount, or quantity, of the motion of 

ect at any instant is found by multiplying its velocity 

. ■•>. when this quantity is to be compared with the 

.atitv of motion of another object. Thus, if one object 

3 much mass as another, and moves three times 

it has six times as much motion. By adopting gen- 

.1 rules of this kind, and then determining one special rule 

each object considered, we become able correctly to cal- 

ite many of its apparent movements in advance. The 

determination of the special rule is called the determination 

of the object. In studying the physical sciences, 

we do not need to consider whether the rules sometimes 

•called laws of nature can be proved to be true in any sense 

ept that in which we call them true because they are 

useful guides in foretelling what is to happen (117). There 

are many questions concerning them which belong to logic 

or to other mental sciences, but not to astronomy. 

606. We seldom have occasion to lay down special rules 
about the movements of any particular celestial object, 
except the rule of its mass. But we must occasionally take 
the shape of an object into account as well as its mass. For 

tTiple, the precessional movement of the Earth depends 

ape. In this case, however, we are really consider- 

\ the masses of different parts of the Earth. There is no 

<:ial rule about the Earth's movements which relates 

- shape. 

607. We now come to the law of gravitation, the accu- 
statement and explanation of which was perhaps the 

ntific work ever done. It may be e: I as 

; vcn material object is constantly 
< any otl. material object with a quantity 

I] mot; proportional to tJie product of the 

tional to the square oj the dist 
onsiacrecL This law i mplei to be 

20 



306 Outlines of Astronomy. [Sec. 607. 

readily comprehended at once ; its meaning will grow some- 
what clearer as we go on. 

608. We must first take notice that the law of gravitation 
does not consist, as is sometimes fancied, in an asser: 
that bodies attract each other : it consists in stating 
they attract each other, and it may be stated, as above, with- 
out mentioning attraction or any kind of force. But it often 
saves words and time to use such terms as attraction, force 
of gravity, gravity, or gravitation. 

609. Secondly, we observe that as every material object 
has some bulk, the distances of its various points from 
given point will not all be the same ; while the law 1 

tation requires us to take into account the distances betwi 
objects. But the ob nsidered in astronomy an 

small compared with the d which separate them that 

we may usually 1 the distance between the 

(157) of any two of them to be the same as the distance 
between any point in one to any point in the other. Not 
that this can always be done; on the contrary, such m< 
DientS as those to which ion and nutation are 

could not be explained unl I the law of grav- 

itation as applyil itely to the separate parts of the 

Earth. We may, of coui iny object as divi 

into parts as small as we pL 

610. Suppose two which wc will call A and Z. to 
be moving towards each other under the law of gravitat 
alone. When they are one hundred miles apart, let us sup; 
them to be approaching each other at the rate of ten mil 
second (599). Now if we consider the mass of A equal to that 
of Z, we must consider A to be moving towards Z at the rate 
of five miles a second, and Z to be moving towards A at the 
same rate ; or else we could not consider the quantities of 
motion (605) of A and Z to be the same, as we must by the 
law of gravitation and the law that action and reaction are 
equal and opposite. "But if we are to consider the ma^ 

A to be T *o of the sum of the masses of A and Z. we must 
divide the joint speed of A and Z between them in a different 



Sec. 6io.] Theoretical Astronomy. 307 

,-. and consider A to be moving six miles a second towards 
Z. while Z moves four miles a second towards A ; this will 
make their quantities of motion equal. 

(mi. Now sup-pose that the mass of A is doubled, while 
that of Z remains as before. By the law of gravitation, the 
quantity of motion of each body must now be doubled ; for 
the quantity of motion is to be directly proportional to the 
product of the masses, and this product is doubled if the 
mass of either body is doubled. Since Z has no more mass 
than before, the quantity of its motion can only be doubled 
by doubling its speed ; it must therefore be moving at the 
rate of eight miles a second. Since the mass of A has been 
doubled, its quantity of motion is doubled without any in- 
crease in its speed : the joint speed of A and Z towards each 
other is accordingly fourteen miles a second instead of ten 
miles a second as before. This joint speed, then, is {;* as 
it as at hrst. But the sum of the masses of A and Z is 
also \ * as great as it was before the mass of A was doubled ; 
and whatever figures we use, we shall obtain a like result. 
The joint speed of any two objects, then, under the law of 
gravitation, is proportional to the sum of their masses, while 
the quantity of the motion of either object is proportional to 
the product of these masses. 

612. We will next consider the meaning of the statement 
that under the law of gravitation the quantity of motion of 
either of two objects is inversely proportional to the square 
of their distance. Let A and Z, as we first supposed, be 
approaching each other at the rate of ten miles a second, 
under the law of gravitation alone, when they are one hun- 
dred miles apart. When they are seventy-five miles apart, 
their distance is J as great as we first supposed it. The 
quantity of the motion of either A or Z is therefore the 

' squ • which is £ times f. or y». as great as it was 

en they were one hundred miles apart. As no change 

sed to occur in their masses, the speed of 

I either of them will be reat as it was j and their joint 

speed will be ] '^- : or \j\ miles in a second. 



308 Outlines of Astronomy. [Sec. 613. 

613. Accordingly, if two bodies move towards each other 
under the law of gravitation alone, their speed must be 1 
stantly changing. Still we consider them to have a certain 
speed at every instant as we may consider a railway train, 
soon after it has started from a station, to have a s 

ten miles an hour at some particular part of the tr 
although it may not keep that speed for the smallest frac- 
tion of an inch that can be named. 

614. We have just been considering the movement of 
bodies under the law of gravitation alone. But every mov- 
ing body is also under the law of inertia, and if two bo 
are moving directly towards each other under the law 
gravitation, their movement under this law i tantly 
added to their previous movement according to the lav 
inertia. But bodies are not always hurried together un 
the law of inertia : the effect of this law is often to keep 
them apart, as we shall see by inquiring how Kepler's laws 
(150) result from the general laws of moti 

615. Kepler's first law is only a | :ic much more 
general, which is this : the movement of one body 70//' 

to another, under the laws of gravitation and inertia^ must 
be in one of the conic I.14). To show this obviously 

requires some mathematical study oft!; ns ; but 

without knowing their properties, we may presently get some 
slight notion of what the course of the required argument 
would be if we undertook to follow it. Kepler's second law 
is easier to explain. It is included in the general statement 
that a body turned out of the rectilinear course, a Ion. 
its inertia would carry it, by any force which at different 
instants is always directed to the same point, will so n; 
that the tine connecting it with that point wit I pass r 
equal spaces in intervals of time which are equal to 1 
other. This statement is not so complicated as it looks : 
still, we need a few simple geometrical facts for its proof. 

616. Let us first suppose a body to be moving in two 
directions at once, and consider the resulting movement ot 
any point in that body. A ship, for instance, may be moved 



Sec. 616.] Theoretical Astronomy. 



3°9 



by the wind due westwards at the rate of six miles an hour, 
and at the same time carried due northwards by a current at 
the rate of two miles an hour. Then, if we consider only 
these facts, and no others, we shall regard the ship as driven 
by two forces, the directions of which are perpendicular to 
each other; one of these forces, which we may call the west- 
ward force, being three times as great as the other, which we 
may call the northward force. If we now consider the motion 
of any particular point in the ship during any small interval 
of time, we see that the point it reaches at the end of that 
interval is both north and west of that from which it started 
at the beginning of the interval, butthree times as far west 
as north of it. Representing the points of the compass as is 
usual on maps, the point must accordingly move from A in 
the figure below to D in the same figure, during the same 
time in which the westward force alone would have carried it 
to B, and the northward force to C ; the line AB being meant 
to be three times as long as the line AC, and these two lines 
being meant to be perpendicular to each other. 




617. If we draw the lines AD, BD, and CD, in the figure, 
AD represents the line along which the moving point is car- 
I under the joint action of the westward and northward 
forces, and is called one of the diagonals of the figure ABDC, 
which is called a quadrilateral because it has four sides, 
a parallelogram because it is a quadrilateral each side- of 
rallel to one opposite to it, and a rectangle 'he- 
cause each of its sides is perpendicular to the two to which 
it is not parallel. The area of this rectangle is the amount 
J of surface which it takes in. This area is three tinn 

s it would have been if the westward force had 1 1 1 n 
iter than the northward force J as is clear when we 



3io 



Outlines of Astronomy. [Sec. 617. 



divide it into three equal areas by the dotted lines in the 
figure. The general rule which this example illus: 
that the areas of two rectangles of equal altitude are to each 
other as the bases of the rectangles ; the altitude of a 
gle being the length of either of its sides which we please to 
select, and its base being the length of either of the si 
perpendicular to that the length of which is called altitude. 
This rule may he proved by geometrical reasoning, which 
many people can make out tor themselves ; hut it may be 
found in books on geometry, if it ia wanted. 

618. Let us now suppose that instead of a northward 
there is a force driving the ship somewhat north-westward ; so 
that the point the movement i^\ which we are considering would 
be carried by this north-westward (nice along the line AE in 
the figure below, in the same time during which the westward 




force would carrv it along the line AB. If the westward and 
north-westward f t together, they will jointly carry 

it in this same time over the line AF, one of the diagonals 
of the parallelogram ABFE. The distance (402) betw< 
either of the sides of this parallelogram, and the side parallel 
to it, may be called the altitude of the parallelogram. In 
this case, the base of the parallelogram is the length of either 
of the sides the distance between which is the altitude. If 
we draw lines from A and B perpendicular to AB and reach- 
ing the line of which EF is part, we shall form a n 
A I) DC, of which the length of AB may be called the 1 
and the length of AC the altitude. But the length of AB 
may also be called the base, and the length of AC the alti- 
tude, of the parallelogram ABFE. The area of the paralh 
gram is clearly equal to the area of the rectangle : for the 
rectangle might be changed into the parallelogram by taking 
the triangle ACE from its eastern end, and putting it on its 



Sec. 618.] Theoretical Astronomy. 



3" 



tern end in the place of the triangle BDF. That is, the 
m and rectangle arc equivalent (394)- It is a 
ral rule that every parallelogram which can be consid- 
ered as having the same base and altitude with a rectangle 
equivalent to that rectangle. This rule, too, is proved by- 
simple geometrical reasoning. 

619. Let us suppose a third case, that of a point moved at 
once by a westward and north-eastward force. In the follow- 
ing figure, suppose that the north-eastward force would move 




the point from A to G, while the westward force would move 
it from A to B. Then both together would move it in this 
same time from A to H. AH is one of the diagonals of the 
parallelogram ABHG, which is equivalent to the rectangle 
AKDC. 

620. The lines AB and AC need not be supposed to have 
the same length in either of the last two figures which they 
had in the first figure. But if we consider them to have that 
length, then it is obvious that AE has been drawn longer 
than AC, and AG still longer than AE. In other words, 
oit supposed north-westward force was greater than the 
northward force previously supposed, and our supposed 
north-eastward force was still greater. This shows that 
equivalent parallelograms may differ largely in the length of 

r sides. 

621. We have now to notice that when a ship is moved by 
winds and currents, as we have supposed, the forces which 
move it must be constantly kept up, or it would not keep 
on moving. If the westward force should cease, Of, in < 

: the wind should stop blowing, the 1 the 

air and water would soon put an end to the westward move- 
ment of the ship. In moving westward it wouid push 



312 



Outlines of Astronomy. [Sec. 621. 



towards the west the air and water close to its western side ; 
according to the law that action and reaction arc equal and 
opposite, this air and water would push the ship eastward 
with a force as great as that by which the ship pushed them 
westward ; so that the westward progress of the ship, under 
the law of inertia, would be combined with an eastward move- 
ment, and its westward movement would be slackened. Its 
headway being now less than before, the resistance of the 
air and water would also be less, but would still continue to 
diminish its headway westward, until none was left. 

622. But celestial objects are not known to meet with any 
resistance in their movements ; and if they meet with any, 
it is very little. Accordingly, the force of inertia alone is 
enough to keep them moving, and if any other force is con- 
stantly aiding the force of jnertia, the object moved by these 
forces must be always going faster and faster. In order to 
simplify the proof of Kepler's second law as much as |> 
ble, we shall suppose the force of inertia to be kept up stead- 
ily ; but another force, which we will call the central force, to 
act only at particular times, and to be kept up, when it acts, 
for a time shorter than any time which can be named. 



v \ ; c 


nil / \ 


F ' 


nj ^s/_^*^ 

li 



623. Suppose, then, that a moving point reaches A in the 
above figure, with a speed sufficient to carry it over the line 
AB in one second. If it is now moving merely according 
to the law of inertia, and no other, it will actually reach H in 
one second after it passes A, and C in one second after it 
passes B; BC being of equal length with AB, and being also 



Sec. 623.] Theoretical Astronomy. 313 

the continuation of AB beyond B. When the point readies 
C, let us suppose a central force directed to O to come into 
play and cease instantaneously, as agreed upon in the last 
paragraph. Let this force be great enough to carry the point 
in one second from C to Q, provided it were the only force 
by which the point was moved. This supposition may also 
be put into the following form. When the point reaches C, 
let it begin to move according to some law under which it 
must take the direction from C to O at the rate of the distance 
) in a second of time ; but let this law instantly cease to 
be applicable to its movement as soon as it quits C. We 
have now to consider the direction and rate of its movement 
at the instant when it passes C. By the law of inertia alone, 
it is moving towards H, and would reach H in a second ; 
CH being the continuation of its former course, and equal to 
or BC. By the new law which comes into play at C, it 
noving towards O at a rate which would bring it to Q in a 
>nd. If, then, we draw the parallelogram CHDQ, we see 
: the point, when at C, must be moving in the direction 
. of D, and at a rate which would take it to D in a second. 
v, although its movement towards O stops as soon as 
it quits C. yet it already has acquired its movement towards 
it the rate just named. Therefore, by the law of iner- 
tia alone, it must reach D at the end of a second after it 
passes C. 

^24. At D. we will suppose that the central force again 

acts, and is greater than at C ; so that under this force alone, 

the point would reach T in one second. Completing the 

parallelogram DKET, and repeating our previous course of 

soning, we must place the point at E one second after it 

D. At E, let the central force act again, and be so 

that the point, under this force alone, would pass 

bev id reach W in one second : for we need not now 

su; e we are not dealing with the law of gravita- 

| that there is air. it ( ), or that our central force 

• Id bring the point no farther than ( ), although it always 

ts in the direction \ through O. Completing the 



314 Outlines of Astronomy. [Sec. 624. 

parallelogram EVFW, we find that the point must move to 
F in one second after passing E. 

625. We will now return to the point A, and compare the 
spaces over which the line joining our moving point with 
has been carried by its movement during each second of 
time. The first of these spaces is the triangle OAR ; the 
next is the triangle OBC ; the next is the triangle OCD ; the 
next is the triangle ODE, and the next OEF. Without 
going farther, we will compare the areas of these triaiu 
with each other. We shall find them all equal ; in other 
words, the triangles are equivalent. At first sight, this 
not evident, although we can see that the triangles gain in 
width as they lose in length. But it is not difficult to pr 
them equivalent, if we consider each as half a parallelogram. 
Beginning with OAB, we will consider it as half the parallel- 
ogram ONAB, of which OA is one diagonal, and BN the 
other. We need not stop'to prove the triangle to be half of 
the parallelogram ; this is obvious from the figure, and its 
proof may be discovered by everyone for himself, or learned 
from works cm geometry. In like manner, OBC is half the 
parallelogram O NBC. Let us continue the line ON, which 
is parallel to BC or AB, towards L, and draw AL and BM 
perpendicular to AB. We have now a rectangle AH. ML. 
Let us call the length AL its altitude and the length AB 
base. AL is likewise the altitude of either of the parallelo- 
grams OX AT) and ONBC, since it is the distance between 
the line OL, of which their side ON is part, and the line 
parallel to OL, of which their sides AB and BC are parts. 
The length of BC is the same as that of AB. Hence either 
of the parallelograms is equal in base and altitude to the 
rectangle, and therefore equivalent to it. Hence the two 
parallelograms are equivalent to each other, and their halves 
OAB and OBC are equivalent to each other. 

626. The triangle OCH is likewise equivalent either to 
OAB or OBC, as is evident by the foregoing reason 
(to prove it at length, we may draw a line from C to N, so as 
to complete a parallelogram ONCH, of which OCH is hall). 



Sec. 626.] Theoretical Astronomy. 315 

1 1 is also half of the parallelogram OC1 1 K. Now the 
ODC is half of this same parallelogram, as is evident 

asitler both triangle and parallelogram cut in two by 
line DO. The triangle ODQ is half OQDR, and the 
CDOishalf CHDQ; hence ODQ and CDQ taken 
ther are half OQDR and CHDQ taken together. Con- 
lently ODC is half OCHR, and hence is equivalent to 
:1. But OCH is equivalent to OBC ; therefore so is 
C. Accordingly OAB, OBC, and ODC are all equiv- 
alent. 

ODE is also equivalent to either of these triangles. 

For it is equivalent to the triangle ODK, which is half the 

1 ODKU. To show that ODE is also half this 

n, we consider it as cut in two by the line ET ; 

3 half OTEU, and DET is half DKET. Hence 

►E is equivalent to ODK, which is equivalent to ODC, 

since DK is equal to CD, and in the same line with it; so 

that ODK is equivalent to ODC for the same reason which 

s OBC equivalent to OHC. 

In like manner. ODE is equivalent to OEV ; and if we 

draw OX parallel to EV or WF, we see that OEY is half of 

the parallelogram OEYX and that FOW is half of the paral- 

jam FXOW. Hence OEV and FOW together are half 

of the parallelogram FWEV : but OEF and FOW together 

are likewise half of this parallelogram: so that OEV and 

OEF are equivalent. OEF is therefore equivalent to ODE. 

There are somewhat shorter ways of proving the 

preceding propositions than those here adopted ; and any 

one who knows something of geometry will he able to find 

them. Besides being shorter, they are more general in 

n : so that they may appear more convincing. I kit what- 

r method is adopted, it is now clear that the general rule 

in which Kepler's second law is included (015; may be 

readily proved when the central force acts only for a moment 

at a time, as we have hitherto supposed it to act. whether it 

amounts to nothing, as at B. or has any strength we pit 

to suppose, as at C, D, and E. But in the orbit of any 



316 Outlines of Astronomy, [Sec. 629. 

celestial body, the central force is gravitation, which is al\\ 
acting. This, however, makes less difference than may at 
first be thought likely. 

630. We will suppose, for the present, that the Sun has no 
movement under the law of gravitation, but remains at . 
while other objects circulate around it. It will appear here- 
after that the incorrectness of this supposition does not 



weaken the explanation which follows. The above figure 
represents an ellipse of considerable eccentricity, its centre 
being at C, and one of its foci at F, where we will sup; 
the Sun to be situated. The point P will accordingly mark 
the place at which any object revolving about the Sun in this 
ellipse passes its perihelion, and A the point where it passes 
its aphelion. Suppose this object to be at B shortly after its 
perihelion pa Then its movement, by the force of 

inertia alone, would be directed towards I. and by the force 
of gravitation alone towards F. It will therefore leave B in 
some intermediate direction, nearly that of D. But as soon 
as it quits B at all, no matter how little, the force of gravita- 
tion no longer acts on it along the line BF, but along some 
other line. When it reaches D, for instance, the force of 
gravitation acts on it along the line DF. Thus, although 
the force of gravitation never ceases, it never acts in any one 
direction for any length of time which can be named. The 



Sec. 630.] Theoretical Astronomy. 317 

only way in which we can represent its action to our minds 
impose the ellipse cut up into an immense number of 
little triangles, each like FBD, but as much narrower as we 
please. We can then suppose the moving object to be at- 
tracted to F as it comes to the boundaries between these 
triangles, but to cross each triangle under the force of inertia 
alone. Devices of this kind often have to be used in reason- 
_ but we must be careful not to let them confuse us when we 
3 >rt to them. They form the foundation of all mathematics 
ept simple algebra and geometry ; indeed, we cannot 
wholly avoid them even there. 

631. Considering the ellipse as thus divided into small 
triangles, each of them crossed by the moving object in an 
equal time with that in which any other is crossed by it, we 
have no difficulty in applying the preceding proof of Kepler's 
second law to the movements of the planets. For as each 
triangle is equivalent to any other, any number of them 
taken together in one part of the ellipse will be equivalent to 
the same number of them taken together anywhere else in 
it. FDB, for instance, is the space covered by a vast num- 
ber of them, and is about equivalent to FPO, which may be 
supposed to contain the same number of them. Since the 
little triangles are all equivalent, their width must differ in 
different parts of the ellipse, to make up for their differences 
in length ; so that although the widest of them is narrower 
than any triangle which can be drawn or thought of, others 
must be narrower still than it is. 

The form of the path of a point, moving according 

i to the law of inertia and also constantly moving towards 

1 some other point which is regarded as fixed, will evidently 

depend on the law according to which it moves towards the 

fixed point, and on the speed and direction of its motion 

it came under this law. Suppose, for instance, that 

•n its motion towards the fixed point begins, it is at that 

i point of its rectilinear course which is the nearest to the 

d point. Then it must at this instant be moving in a 

direction perpendicular to that of the line joining it with the 



3»8 



Outlines of Astronomy. [Sec. 632. 



fixed point (402). Now suppose the law under which it i 
move towards the fixed point to be such that the speed of 
this motion will not change as long as the distance between 
the moving and fixed points remains the same. It may s< 
at first that if one point moves towards another at all 1 
distance cannot remain the same ; but what has been said of 
the resolution of movements into others, both in this chapter 
and previously (114), will show that there is nothing absurd 
in the supposition just made. Let us also suppose that the 
law of the movement of the moving point towards the fi 
one gives the moving point a speed, when it first comes 
under the law, so proportioned to the speed it previously 
had, that its Course is changed just enough to keep it from 
getting farther from the Ux^il point, as it would do, accon 
to our supposition under the law of inertia alone, and would 
do still more quickly after its speed had been increased 
the addition of a new movement in a direction perpendicular 
to that of the first ; this must of course be taken into account 
in considering how much change of direction is ry in 

the motion of the moving point to keep it as near the fixed 
point as it was when this change of dire* 
Although we cannot here enter into a calculation of this 
kind, it is clear from the following figure that the mo\ 

i point m.i w as 

well as too fast in its mo- 
tion towards the fixed point, 
always to remain at the same 
distance from it. If the 
fixed point is at F, and the 
moving point has reached 
M from L. it would go on 
to A under the law of in- 
ertia alone ; but if it b< 
at M to have a movement 
towards F, it may cross the 
line FA at any point between F and A. : it turns into the 




course MB, it will be farther from F at B than it was at 



M: 



Sec. 632.] Theoretical Astronomy. 319 

if it turns into the course MC, it will be as far from F at C 

ls at M : and the course MC may be such that all its 
[ually far from F. In this case the moving point 
will continue to go round the circumference of a circle, the 
centre of which is at F, provided that the law under which 
movement towards F takes place does not change the rate 
of that movement as long as the distance between F and the 
moving point remains unchanged. The law of gravitation is 
a law of this kind. Accordingly, it is theoretically possible 
that one point should go round and round another in an exact 
circle, under the laws of inertia and gravitation alone. But 
it is plainly very unlikely that an instance of such a move- 
ment should occur. 

Let us next suppose the moving point to cross FA 
veen A and C. Its course is now taking it farther and 
farther from F. Now if the law under which it is moving 
towards F is the law of gravitation, the rate of this move- 
ment is lessening ; so that the moving point may perhaps 
always keep on increasing its distance from F. It will then 
be moving in a hyperbola or a parabola, most likely a hyper- 
bola. This follows from the geometrical properties of these 
curves and from the exact terms of the law of gravitation ; 
under another law we might have some other result. 

634. But it does not follow that under the law of gravita- 
tion the moving point miTst always go on increasing its dis- 
tance from F, even if it crosses FA between A and C. To 
understand this, we must notice that if it is at any time in- 
Creasing its distance from F, its movement may be resolved 
into two, one directly away from F, and one in a direction 
endicular to the first. The first of these movements is 
cavitation ; and when a movement is composed of 
the dire which are perpendicular to each other, 

it is lessened if either of the movements which compose it 
lied (617). The whole movement of our supposed 
point i.> tl e ravitatioo ; so that 

rom F. \'<m although 
^ment under the law of gravitation diminishes as its 



320 Outlines of Astronomy. . 634. 

distance from F increases, yet as its movement under the 
law of inertia is also slackening, the comparative great 
of these changes must decide whether, after ent time, 

the moving point does not ce farther from F. It 

may at length reach a part of its course where it 
moving in a direction perpendicular to that of the line join- 
ing it with F. In this case, its movement under the la . 
inertia must have been so greatly reduced that its movement 
under the law of gravitation afterwar 
nearer and nearer F. 

635. Hut as it approaches F, its sp« -mtinually 

increased, for a Like reason to that for which its speed has 

previously been Lessened Its movement under the law 

inertia at Length overbalances its movement under the lav 
gravitation, in spite of the increase ^i this last movement 
it comes nearer to F ; and it again passes the point M with 
the same speed and in the same direction as b< 
ing its movement along an ellipse, the point of which situated 
at M answers to the point of the orbit of a planet where the 
planet's perihelion passage takes place. 

The proof of this depends on the pr< if the 

ellipse and the strict statement of the law of gravitation. 
Fut if we admit it to he true, we see that if the moving point 
crosses FA between A and C, it may continue to circulate 
about F in an ellipse of which I* is one focus tl 
focus being in the direction from M to I'", hut beyond F, 
Hence, if the movement of the moving point under the law 
of gravitation is not great enough compared with its mo 
ment under the law of inertia to make it revolve about F in 
a circle, its path may be either an ellipse, a parab 
hyperbola, according to circumstances ; but I in 

either path can never be so great at any other point in its 
course as at M. 

637. If its movement under the law of gravitation is too 
great, as compared with its movement under the 1 iw of inertia, 
to allow its path to be circular, it must move in an ellipse; 
but in this case the ellipse is smaller than before, and F is 



637] Theoretical Astronomy. 321 

that one of its two foci which is farthest from M ; so that the 

the moving point is less at M than anywhere else in 

>rbit. If its orbit is circular, its speed in that orbit must 

uniform by Kepler's second law. If, when it first comes 
under the law of gravitation, the direction of its movement is 
not perpendicular to that in which it is to move under the law 

cavitation alone, its path cannot be circular, but may be 
an ellipse, a parabola, or a hyperbola, according to circum- 
stances. The rules just laid down will be stated more accu- 
at the end of the sixteenth chapter. 
We have been supposing that the Sun remains fixed, 
while some other object circulates about it (630). Let us now 
inquire how two bodies, to both of which the law of gravitation 
applies, will move with respect to each other. The quantities 
of motion of both bodies, under the law of gravitation alone, 
must be equal ; and if we suppose their masses equal, their 

cities will also be equal (610). Now. if they begin with 
no motion at all except under the law of gravitation, they will 
move directly towards each other ; but any other motion they 
may have at first in other directions will throw each into some 
kind of orbit about the other. Let us suppose their original 
motions equal, perpendicular in direction to the line joining 
the two bodies, opposite to each other, and just quick enough 
to keep the bodies from approaching each other. Then their 
orbits will be circular, and they will move equally fast in those 

its, so that they may be regarded as always at opposite 
ends of some diameter of a circle round the circumference of 
which they are both moving. In this case each of them may 
be considered as revolving, not about the other, but about a 
fixed point half-way between them. In other cases, which are 
imple, it is likewise found by the proper calculations 
that each of the two bodies moves about a point somewhere 
between them, and that this point is fixed. SO far as the 
movement of the two with respect to each other is 

concerned, although we may of course suppose it to be 
tlong in any movement which the two bodies may 

itly have with r 1 point is usually 



322 Outlines of Astronomy. [Sec. 638. 

called the centre of gravity of the two bodies. The orbits 
of the two bodies about their centre of gravity will be alike 
in shape, however much they may differ in size. If we regard 
either body as fixed, and examine the path of the other with 
respect to it, we shall find the shape of this path also to be 
like that of either of the bodies about their centre of gravity ; 
while its length is as great as the joint length of the two 
separate paths of the bodies about that centre. The speed 
of either body, when regarded as moving about the other, 
must likewise be the same, at any particular moment, with 
the joint speed of the two bodies at that moment, when they 
are considered as moving about their centre of gravity. Each 
body will be nearer the centre of gravity in proportion to the 
itness of its mass as compared with the mass of the other 
body ; and its orbit will be smaller, and its speed less, in the 
same proportion. 

639, If there were no bodies in the Solar 1 xcept 

the Sun and the Earth, we might consider the Sim as revolv- 
ing about the Earth. But when we notice that the move- 
ments of the other planets, as seen from the Earth, can be 
best accounted for by supposing them all, and the Earth 
likewise, to revolve in ellipses about the Sun, we see that 
according to the law of gravitation we must suppose the 
Sun's mass to 1 it in comparison with that of any 

other body in the Sol lr System that its movements within 
that system are to be regarded as very small. The law of 
gravitation thus makes Kepler's first law appear as a par- 
ticular case occurring under a more general law ; while 
Kepler's second law likewise appears in a more general 
form. The fixed point, towards which the central force 
acting on any planet is directed, is the centre of gravity 
of that planet and the Sun, when we disregard the action 
of the other planets, as we find in practice that we may 
(170). We may also regard the Sun as fixed, which will 
slightly increase the speed to be attributed to the planet, but 
will leave Kepler's second law still strictly applicable to its 
movements. 



Sec. 640.J Theoretical Astronomy. 



323 



640. The following figure, the scale of which is smaller than 
of the last figure, F being 

nearer to M, will show the 
forms of the various orbits 
mentioned above. Mil is part 
of a hyperbola ; MP part oi a 
parabola ; ME an ellipse with 
its foci at F and f ; MC a cir- 
cle with its centre at F; MI 
an ellipse with its foci at F 
and/! Ellipses with their foci 
as far from the ends of their 
r axes as those here rep- 
uted can hardly be distin- 
guished from circles. 

641. We have now seen what 
general course of reasoning 
must be followed to arrive at 
the conclusion that, under the 
laws of gravitation and iner- 
tia, the path of either of two 
bodies which we please to con- 
as moving about the other 

will be one of the conic sections (615). The convenience of 
irding one or the other body, or both of them at once, as 
moving, depends on the comparison of their masses (638). 
have also seen why it is convenient, in forming a general 
v of the movements which occur among the bodies of the 
Solar System, to consider the Sun as fixed, and the planets 
•noving only around the Sun and not at all around each 
other. However, when accuracy is necessary, we take into 
account, in considering the movement of any one planet, 
the slight changes in its orbit occasioned by its place with 
ect to other planets. These changes are called pertur- 
bations (170). 

Satellites are so near the planets to which they are 
>idered as belonging, that it is most convenient to reg ird 




3 2 4 



Outlines of Astronomy. [Sec. 642. 



them as moving around their planets, and subject only to 
perturbations by the Sun ; although the attractive force of 
the Sun may actually be greater on a satellite than is that 
of the planet to which it belongs. 

643. Comets, as we have seen (232), are usually consid- 
ered to move in parabolas ; but this means that we usually 
see so small a portion of a comet's orbit that the shape of 
the whole orbit cannot be exactly determined. 

644. Kepler's third law can be proved without much diffi- 
culty if we suppose it applied only to orbits which are exactly 
circular. But even for this partial proof, we need a few g 
metrical propositions, in addition to those already explained. 
First, the angles of every plane triangle^ taken : 
amount to 1S0 (419). The most obvious proof of this 
obtained by considering how much movement of rotation 
is enough to bril light line into the direction of each 
of the sides of a plane triangle in turn. In the follow 
figure, for instance, let part of the line MX coincide with the 

AB of the triangle 

ABC ; then let M 
tate on an axis 
through A and perpen- 
dicular to the plane of 
the triangle, until part 
of it comes into coinci- 
dence with AC ; M will 
then be at ;// and X at ;/. 
By a similar rotation on 
an axis passing through 
C, part of MX may next 
be brought from its new position to coincidence with BC; 
and a final rotation on an axis passing through B will bring 
part of MN to a new coincidence with AH. M being now at 
M' and N at N\ so that the last direction of MX is contrary 
to its first direction. It has therefore been turned half round ; 
or, in other words, it has been turned through 180 . But in 
its first rotation it was turned through the angle BAC, in its 




Sec. 644.] Theoretical Astronomy. 



325 



second rotation through the angle ACB, and in its third rota- 
through the angle ABC ; hence these three angles amount 
to 1 So . This proof, like all other proofs of the same propo- 
-n, depends on taking certain facts about straight lines 
granted. These facts are not disputed ; but what is the 
way of stating them has never yet been settled. One 
. is that which has been adopted above, in the chapter on 
geometrical terms. 

Next, if each angle of either of two plane triangles is 
equal to one of the angles of the other triangle, the compar- 
ative length of any two sides of either triangle is the same 
the comparative length of the two sides of the other tri- 
ple, the angle between which is equal to that between the 
sides first chosen. This may be stated more briefly as 
follows : if the corresponding angles of two plane triangles 
equal, the sides including those angles are proportional. 
In the next figure, the angle at 
D of the small triangle is meant 
to be equal to the angle at A of 
the large triangle ; the angle at 
E equal to the angle at B, and 
the angle at F equal to the angle 
at C. Hence, according to the 
proposition just stated, D£ must 
be the same fraction of DF that 
AB is of AC. If AB is just 
seven-eighths of AC, then DE is just seven-eighths of DF. 
If a piece of paper is cut into the shape and size of DEF, 
and laid on the upper part of ABC, so that D may fit A, it 
will depend on which side of the paper is uppermost whether 
E comes to e and F to f or E to e and F to /. Let us take 
the first of these arrangements ; then as the angle E is 
equil to the angle B. the line ef will be parallel to BC If 
we meisure off the line AB into lengths each equal to Ae, 
and AC into lengths each eqi it is p] iin thai there 

will be the same number of lengths and the same fraction of 
a length in AB and in AC. The full proof of this may be 




326 



Outlines of Astronomy. [Sec. 645. 




found in works on geometry, where it is also shown that it 
follows, as almost any one can see for himself, that Ae is con- 
tained in Af as often as AB in AC. 

646. We shall also require the proposition that .' 
meeting on the circumference of a circle, and passing thro., 
the ouis of one of its diameters, must be perpendicular to 
each other. In the next figure, let the two lines BA and . 

meet at A. and let HI) be a diameter of 
a circle having A in its circumference. 
The centre of this circle will he at C, half- 
way from B to D. If we draw the line 
CA, we shall have two triangles . 

I), each of which has two of its sides 
radii of the circle, and tin; h other. Hence 

the angles Opposite these sides are likewise equal to each 
other ; that is, tin is equal to AB< ', and the angle 

CAD equal to CDA. The proof of this i 

not be given here. Hence the sum of BAC and < 
the angle BAD, is equal to the sum of ABC and CDA. 
But all these four angles ther equal to 1X0 , since 

they make up the three angles of the triangle ABD. Hence, 
BAD is an angle of 90° ; in other won!-, \V> is perpendicu- 
lar to AD. 

647. We must next apply the results just obtained to the 
study of movement in circular orbits. Let the arc bet* 

M and B in the anni re be 

part of the circular orbit of a m< 
point about another point fixed at 
O. If the moving point went on 
from M under the law of inertia 
alone, it would go towards A instead 
of B. Suppose the distance from 
M to A to be equal to the l< 
of the arc between M and R : then 
the distance between A and B shows 
nearly, but not exactly, how far the moving point has trav- 
elled under the law of gravitation alone in the time which it 




Sec. 647.] Theoretical Astronomy. 327 

ipies in passing from M to B. If we draw a line from 

endicular to the line from O to B, and meeting it at P, 

distance from B to P is nearly the same as that from B 

A. But, as is shown by the additional lines of the figure, 

if the arc between M and B were made longer, there would 

be more difference between the distance from A to B and 

that from B to P ; and also more difference between either 

of these distances and the distance travelled by the moving 

point under the law of gravitation alone in the time during 

:h it moved over the arc. In fact, these differences grow 

disproportionately great as we take larger and larger arcs 

into account ; while if we take smaller and smaller arcs into 

account, the differences dwindle away much faster than the 

arcs : so that when the arc is smaller than any arc which can 

be named, the differences are a smaller fraction of this small 

than any fraction which can be named. To understand 

this thoroughly, some mathematical knowledge is wanted ; 

must here take the fact on trust. Any error, then, which 

we may make in our calculations, by supposing the distance 

from B to P to be the distance through which the moving 

point passes under the law of gravitation alone while it 

moves from M to B, may be remedied by supposing the arc 

between M and B to be smaller than any arc which can be 

named. In like manner any error may be corrected which 

may result from our considering the distance between M and 

B equal to the length of the arc between those points. 

The triangle DBM has a right angle at M (646) ; and 

the triangle MBP has a right angle at P, since P is the point 

ere a line drawn from M perpendicular to the line from B 

3 that line. Both triangles have the same angle 

at I as the triangle MBP has two of its angles equal 

f those in the triangle DBM, and as the angles of 

h triangle taken together, amount to 1 So (644). the third 

*le of the triangle MBP must be equal to the third angle 

the triangle DBM: ^o that the triangle MBP mighl be 

and placed with its point P at p and its point B 

point M coinciding with D. In the triangle MBP, 



328 Outlines of Astronomy. [Sec. 648. 

the distance from B to P is a certain fraction of the distance 
from M to B ; and in the triangle DBM, the distance from 
M to B is a certain fraction of the distance from D to 
These two fractions are equal (645). 

649. We must now state these facts in algebraic lang 

or our reasoning would not be clear, owing to the number of 
words it would require. Readers unacquainted with algebra 
need only be told that each letter used as an algebraic sym- 
bol stands for some number which need not be precisely 
stated, because its value remains the same throughout the 
whole of the course of reasoning in which it is employed. 
Letters written together denote the product of the numbers 
for which they stand, and this product is to be multiplied by 
any number placed before the letters ; thus. 2<i/> stands 
24 if a denotes 4 and /> 3, or for 60 if a denotes 5 and b (). 
It makes no difference in what order we write the factors of 
a product ; and instead of repeating a letter or a number. \\i 
may denote the number of times it is used a- a factor by a 
number called an exponent : thus we may write 2* instead of 
4, which is the product of 2 by itself: and instead of abcabd 
we may write aWcd. $cd multiplied by yn\ and this product 
multiplied by 3/V. may be expressed by 3V/',' 1 //, or 
In an algebraic fraction, the denominator is considered as 
a divisor, and the numerator as a dividend ; a factor com- 
mon to both numerator and denominator may be struck out: 
the fraction is multiplied by multiplying its numerator or by 
dividing its denominator, and divided by multiplying its 
denominator or by dividing its numerator ; all these rules 
being exactly the same as those of arithmetical fracti* 
The sign = shows that the two expressions between which 
it stands denote numbers which are equal to each other. 

650. Let / stand for the number of seconds required for 
one complete revolution of the point which we supposed to 
move in the circumference of the circle in our last figure 
(647) ; and let r denote the number of feet in the radius of 
the circle. Then the number of feet in the diameter of the 
circle will be denoted by 2r, and the number of feet in its 



Sec. 650.] Theoretical Astronomy. 329 

circumference by about JJj of 2/\ or more precisely by 2irf 

(41 ;). Accordingly, since the point moves at a uniform rate 

. the number of feet which it traverses in one second 

will be the number ot times that 2nr contains /: and we 

this in the form of the fraction ' . Now if we 

i the number of seconds in which the moving point 

:e MB (which we have agreed to consider 

equal to the number oi seconds in which it traverses the arc 

we may denote the number of feet in the arc MB by 

lich may denote a very small fraction of one foot, iff 

denotes a sufficiently small fraction of one second, however 

e the number -- mav be. 

651. Let g stand for the number of feet traversed by the 
moving point, in the time /, under the law of gravitation alone ; 
we have agreed to consider this equal to the number of feet 
in the distance BP. It follows from the equality of fractions 
obtained above (648) that if we divide g by ^^. and ^! 

the quotients will be equal. The second of these 
nts is to be denoted, in accordance with our rules, by 
-. If we multiply each quotient by *—^ the products will 
be equal, by the ordinary rules of arithmetic. The result of 
first dividing and then multiplying g by — ' is to leave its 
value unchanged ; accordingly g is equal to the product of 

*/ 1 2~ri .... 2ir-r/ i 

- by — , which is — — . 

652. Let us now suppose a second point moving in a circle 
than that the radius of which contains the number of feet 

denoted by r, but moving, like the first point, under the laws 

.itation and inertia, round a point fixed at the centre of 

the larger circle. If we denote by T the number of seconds 

in which this point goes once round the circumference of its 

and by R the number of feet in the radius of that 

we may show, ; it the number oi 

!in the time i by the second moving point, under 
the la itation al 

653. Let us also suppose the 1 lies at the 



3$o Outlines of Astronomy. [Sec. 653. 

centres of the two circles to be equal to each other, and the 
masses of the bodies to which the moving points belong to be 
equal to each other. The movements of the moving points, 
under the law of gravitation alone, must then be invers 
proportional to the squares of the numl in d 

R. That is (612;, it" we divide ^p- b; the quotieat 

will be equal to that of R 2 divided by r*. The arithmetical 
rule for the division of one fraction by another is to multiply 
the numerator of the dividend by the denominator of the divi- 
sor for the numerator of the quotient, and the denominator of 
the dividend by the numerator of the divisor for the denomi- 
nator of the quotient ; a rule which plainly follows from the 
general rules for fractions (f>4<;). Our result, according 
will be 2n . r ' ,, = \. Striking out the common factors 

r- 

27rV 2 in the numerator and denominator of the first fraction, 
we have ^, = -. Multiplying each of these equal numbers by 
R and dividing each by )\ we have which is Kepl< 

third law (150) expressed algebraically, on the assumptions 
that the orbits considered are circular, and that the bodies 
moving in them have so little mass compared with th< 
body that their masses may be considered equal, and the 
central bodv regarded as at rest. The assumption that the 
orbits are circular is not necessary; it has here been made • 
on account of the difficulty of the geometrical propositions 
required to prove Kepler's third law for elliptical, parabolic, 
and hyperbolic orbits. The second assumption may properly 
be made when we are studying the movements of the planets, 
unless we require our conclusions to be very accurate ; for 
the mass of the Sun is more than a thousand tin 
than that of Jupiter, the largest of the planets. 

654. We can now understand how the m any celes- 

tial objects, or the special rules of motion relating to them 
(605), are to be ascertained. The speed with which two mate- 
rial objects approach each other, under the law of gravitation, 
depends, as we have seen (611), on the sum of their m 
Let us go back to the expressions — -— and ~ 



Sec. 654.] Theoretical Astronomy. 331 

denote the numbers of feet which our two moving points 
erse in the time /.under the law of gravitation alone ; and 
let 1 1 of the n the body moving in 

the large circle and the body fixed at the centre of that circle 
ntained in the sum of the masses of the other pair of 
l certain number of times, which we will denote by //. 
The movement of this other pair of bodies towards each 
other, or of either body towards the other, regarded as at rest 
;8), will then be // times quicker, with respect to the move- 
ment towards each other of the bodies of the first pair, than 
we previously supposed it to be. Therefore, if we now divide 
-£- by 2 "'J\ our quotient will be // times as great, with 

■ect to the quotient --, as it was before. We have, then, 
- = ' '— -. or = ^- ; and multiplying each of these equal 

T'-V 3 

quantities by r 1 an 1 dividing each by R\ we have — = //. 

655. Hence, if we know the distance between two objects, 
the time in which either revolves about the other (638), and 
the distance and time answering to these in the case of 
another pair of objects, the movement of each pair not being 
•jet to any important perturbations (641), we can find 
how many times the sum of the masses of one pair is con- 
tained in that of the other. Indeed, it is only the difficulty 
of the mathematical operations required when the orbits to 
be considered are not circular and are subject to very large 
perturbations, that keeps us from determining the compara- 
tive masses of any three bodies circulating about each other 
and not subject to other perturbations than those which each 
of them occasions in the movements of the other two. For 
three bodies may be considered as arranged in either of three 
rm a pair of bodies with one left over ; from 
the letters a. h. c, for instance, we may form the pairs nb. h L \ 
tically, however, we have to confine OUHU Ives to such 
^e which rved in the Solar Sys- 

tem. That is, the comparative masses of three bodies can 
mined when they can be so arranged in pain 
I the movements of the bodies of each pair with respect to 



332 Outlines of Astronomy. [Sec. 655. 

each other are altered only a little by the place of the third 
body. 

656. We shall naturally begin our inquiry into the masses 
of celestial objects by comparing the mass of the Earth with 
that of the Sun. The most direct way of making this conV 
parison is to take some small piece of the Earth itself, such 
as a leaden weight, tor the third body which will be required, 
as we have seen, to carry out our purpose. This weight will 
have no mass which is noticeable in comparison with the 
mass of the Earth ; and in our experiments with it, it will 1 1 
close to the Earth that its movements with respect to other 
bodies will be practically equal to those of the Earth its 
Hence we shall neither have to consider that the Earth me 
nor that the weight m ept with rth. 

657. We will first suppose that we can make the weight 
circulate about the Earth, near its surface, under the 1 

of gravitation and inertia alone. We are then t the 

distances from the Earth's centre to the weight in its various 
places, and also to observe how much time the weight re- 
quires to go once round the Earth. We know the time (called 
the sidereal year, 507, 574) in winch the Sun apparently 
volves about the Earth ; and we also know about how far the 
Sun is from the Earth. Thus we obtain the number of times 
that the sum of the masses of the Earth and the weight, which 
is practically the mass of the Earth, is contained in the sum 
of the masses of the Earth and the Sun. To make our cal- 
culation a little more accurate, we ought first to determine 
the mass of the Moon ; for the Moon may be considered . 
part of the Earth, so far as the Earth's revolution about the 
Sun is concerned. Since the Moon is so much nearer the 
Earth than the Sun is, the movements of both Earth and 
Moon with respect to the Sun are very much alike ; hence 
we may use the process just described in finding, first, how 
the mass of the Earth compares with the sum of the mass 
of the Earth and Moon ; and next, comparing this sum with 
the sum of the masses of the Earth, Moon, and Sun ; the 
Earth and Moon being considered as one body. 



Sec. 65S.] Theoretical Astronomy. 333 

65S. We may compare the sum of the masses of the Earth 
and Moon with the sum of the masses of the Earth, Moon, 
and Sun, by taking the Earth and Moon for our first pair of 

ies, without using the weight which we have supposed to 
Circulate around the Earth ; in this way. however, we should 

be able to compare the mass of the Earth separately with 
that of the Sun. The mass of the Moon, in practice, is best 

rmined by means of the facts of precession and nutation. 
The distance of the Sun, and hence the length of the Earth's 
orbit, is not yet known accurately enough to allow us to 
determine the masses of celestial objects with great preci- 
sion. Hence it is practically needless for us to distinguish 
between the mass of the Earth and the sum of the masses of 
the Earth and Moon, as we have done above. 

659. Although we cannot make any thing revolve about the 
Earth like a satellite, we can learn how fast it would revolve 
at any given distance from the Earth, by noticing the rate at 
which it falls, when it is lifted from the ground and let go. 
It is not easy to observe this rate directly, but it can be 
ascertained in various ways ; in particular, it may be calcu- 
lated from the rate at which a pendulum swings. Our 
knowledge of the comparative masses of the Sun and the 
Earth has been gained, to a considerable extent, by counting 
the number of times that a pendulum of known length will 
swing during a given interval. The part of the Earth at 
which the experiment is tried makes a difference in the 

it, which has to be allowed for by calculation (160). 

m these observations and calculations we obtain our 
special rule of movement in the case of the Sun (605). This 
rule, as we have seen (47), is, that any movement of the Sun 
must be considered some 320.000 time it as a mo 

t made ' irth through the same distance : just as 

the movement of 320.000 quarts of water through 01, 
to 1 red 320,000 times I a movement as that 

of I fjuart of water through one I 

660. The masses oft! • 'f the Solar S . 

are usually expressed in fractions of the mass of the Sun. If 



334 Outlines of Astronomy. [Sec. 660. 

a planet has satellites, the joint mass of the planet and its 
satellites may be compared with the mass of the Sun in 
manner just described. It" it has no satellites, its mass must 
be ascertained exclusively by the small perturl 
it produces in the orbits of other planet these n 

ods are available in the case of the planets Jupiter. 
Uranus, and Neptune. The masses of planus which 
too small to occasion noticeable ] ons in the or' 

of other planets, cannot 1) determined. Some- 

thing has been learned of the masses of Jupit< lites 

by the effects produt 1 tellite on the movement of 

the others. \\' t also know that the sum of the i t" the 

asteroids cannot be great in comparison with the Earth's 
mass ; but the in ny individual asteroid is unknown. 

The ma forming a binar 

can be determined from the rates at which they move: but 
the- annot be known unless we know the 1 

between the two ivm times : to know this d 

again, we must know the distances of tl from the 

Earth ; but these (lis: ' !<>m known at all, and 

no case known ly. Hence we have on!' 

knowledge of the masses of tl ; but it is likely that 

these ma I that of the Sun (So). 

662, In order to compare the miss of a celestial 
with that of a cubic foot of lead, or of a quart of quit 

we must first know what fraction this is of the Earth's m 
This can be learned in various ways; and the results ob- 
tained by different methods a<^ree together better than WO 
have been expected. We find that the Earth's mass is cqu d 
to that of a body of the size of the Earth, having in all 
parts 1 density about five and a half times 
of water. According to this the number of tons of 
in the Earth would be roughly expressed by the figure 6 
followed by twentv-one ciphers. 

663. The most direct method of comparing the Earths 
mass with that of a leaden ball is to balance a small weight 
very delicately and measure carefully how far it will change 



Sec. 663.] Theoretical Astronomy. 335 

place when the leaden ball is shifted from one side of it to 
rther. This is called the Cavendish experiment. Other 

hods are the observation of the rates at which a pendu- 
lum will swing in a deep mine and on the surface of the 

th, or on the top of a mountain and at the sea level ; also 
the alteration of the vertical line, as determined by a sus- 
pended weight, on opposite sides of a mountain. But in the 
u>e of these methods the density and extent of the layers of 

x near the place where the experiments are tried must be 
known : and this cannot be completely discovered. 

664. A statement of the Earth's mass in tons, like that 
just given, has not a perfectly distinct meaning. A ton is 
the name of a certain weight ; now the same body has some- 
it different weights in different parts of the Earth, 

although its mass always remains the same. So long as we 
continue to weigh one body against another, their compara- 
tive weights will be the same wherever we may take them. 
But if we weigh a lump of lead, at different terrestrial places, 
h a spring balance of sufficient delicacy, we shall find that 
weight is less, or, in other words, that it stretches the 
spring less, the nearer we bring it to the equator. This 
ct depends, as we have seen (160), on the varying distance 
of the body which is weighed from the centre of the Earth, 
and on the increasing rapidity of the Earth's rotation as we 
approach the equator. 

665. Hence two bodies of equal mass situated on different 
planets must have different weights. At the surface of the 
Sun. the weight of any object would be about twenty-eight 
times what it is at the surface of the Earth. In a deep mine, 
the weight of every thing is slightly greater than its weight 

a it is taken to the mouth of the shaft : hence a pendu- 
lum quicker the deeper into the Earth it is taken. 
so that it may be used, as just stated, for determining the 

The direction of the vertical li; like.' the 

a : for the determination of this line at any 

terrestrial place obviously depends upon the form of the 



336 Outlines of Astronomy. [Sec. 666. 

Earth and the density of its various parts. If a large moun- 
tain, for instance, is north of the place of observation, what 
appears to be a vertical line will point south of the zenith 
and north of the nadir which would have been found if the 
land to the northward had been low. To understand I 
we need only remember that the reason why a weight when 
let fall, drops nearly towards the centre of the Earth, is that 
this must be the result of the various movements which it 
has towards all parts of the Earth at once, under the l.r 
gravitation. But as it moves most rapidly towards the m 
est parts of the Earth, it may be slightly turned from its 
course by a neighboring mountain or by t! 
of the ground on one .side than on another of tin liere 

it is let fall. If the vertical lines found by observation in 
different parts of the Earth all crossed each otll ■ one 

point, we might call this point the Earths centi \ity. 

But in tact they do not meet in any one point, although none 
of them pass very far from tin- middle of the Earth's a 
The general form of the Earth has usually much nn 
on the determination of vertical lines than is produced hy 
Unequally dense or uneven ground. As the polar diam< 
of the Earth is the short* ight let fall at aln 

any place north of the equator will come to the ground a 
little to the south of the place where it would have fallen if 
the Earth had been exactly spherical. Hence, as a 
rule, the zenith 1515) determined by observation, anywhere 
north of the equator, will be a little north of the point whi 
a line from the Earth's centre through the plac< 
tion would pierce the celestial sphere. In the southern 
hemisphere the observed zenith will be south, instead of 
north, of the corresponding point of the celestial spi. 
Now as every terrestrial latitude is determined from the 
observed zenith of the place where the observations are 
made (542), this geographical latitude, as it is called 
little greater than geocentric latitude, or the angle between 
two lines from the Earth's centre in the plane of the local 
meridian, one drawn to the equator and the other to the 



Sec. 666.] Theoretical Astronomy. 337 

place of observation. Geocentric latitude and geographical 
latitude agree, however, at the poles and at any place on the 
equator. 

Suppose that we know the length in miles of one 
quarter of a terrestrial meridian (517). measured along the 
: >) of the various parts of the Earth from one of 
the poles to the equator. If two points on this quarter 
meridian, and near the equator, differ in geocentric latitude 
the number of miles in the distance between them 
must be a little greater than the number of miles between 
places on the same quarter meridian, and near the pole, 
which likewise differ by i° in geocentric latitude ; because, 
r the pole, the line on which the measurements are made 
- comparatively near the centre of the Earth, and there- 
- the lines which form the sides of the angle of 
latitude before they have spread apart as far as they have at 
the distance of the equator from the Earth's centre. But 
e the geographical latitude of a place is a greater angle 
than its geocentric latitude, except on the equator and at 
the poles, it follows that as a traveller goes from the equator 
- either of the poles, his geographical latitude must 
at first be increasing faster than his geocentric latitude, but 
after a time must increase more slowly than his geocentric 
latitude, so that the two kinds of latitude may each come to 
OX) 3 at the same time, when the traveller reaches the pole. 
Hence if two places near the equator differ as much in geo- 
centric latitude as two places near the pole, they will differ 
more than the two places near the pole in geographical lati- 
This may result and in fact it does result, in making 
the number of miles between two places on the same merid- 
ian, and near one of the poles, greater than the number of 
j miles between two places on the same meridian, and near the 
1 equator, when the difference of geographical latitude be- 

Ien the tw of each pair is the same. 

668. The ri^.ire of the Earth maybe determined, then 
determining the latitudes of a number of places at differ- 
ent distances north or south of the equator, and then survey- 



338 Outlines of Astronomy. [Sec. 668. 

ing the distances in miles between some of these places and 
others near them, which need not be exactly on the same 
meridian, because their differences of longitude can be al- 
lowed for in the calculations. The latitudes of the places 
are determined by astronomical observations (542) ; the dis- 
tances from each other of the places to be connected by any 
particular survey are found by first measuring a line some 
few miles in length, called the base of the survey, and meas- 
uring the visual angles between various terrestrial objects 
seen from the ends of this base. This enables the distances 
of the objects observed from the ends of the base to be cal- 
culated : and thus the length of many lines much longer than 
the base itself becomes known without the need of actual 
measurement. These long lines may now be used to deter- 
mine others ; and a network of imaginary lines is thus - 
by degrees over the face of the country surveyed, until the 
distances in miles between any two places in it can be 
with all the accuracy which may be required. All this 
is of the same sort as the determination of the distances of 
celestial objects by means of their parallax. It is useful for 
many purposes besides that of the determination of the shape 
and size of the Earth. It enables us. for instance, to make 
accurate maps of the coast or of the inland parts of any coun- 
try which has thus been surveyed. 

669. The Earth's precessional movement, like the * 
tions of the weight of terrestrial objects and those of the 
length of different of latitude, is due to its shape. 

One conclusion to be drawn from the law of gravitation is 
that a perfect sphere, of uniform density throughout, will 
move as if its whole mass were compressed into a mere 
placed at its centre. A body of this kind would have no 
precessional movement. But when the Moon is north of the 
plane of the equator, the equatorial parts of the Earth on 
the side next the Moon are so much nearer the Moon than 
the parts answering to them on the opposite side of the 
Earth that they get a slight northward movement with re- 
spect to those opposite parts ; this tilts the Earth slightly, 



Sec. 669.] Theoretical Astronomy. 359 

that if its movement of rotation did not constantly change 
the side of it which faces the Moon, the angle between the 
plan equator and that oi the Moon's orbit would begin 

liminish. According to the law of inertia, however, this 

not actually happen : and instead of rocking on an axis 
rpendicular to the line joining it with the Moon the Earth 

- the peculiar twisting movement to which precession is 

due. If the Moon is in the plane of the Earth's equator, it 

for the moment, to change that plane; and at other 

'aether it is north or south of the equator, its action 

ontinually varying ; but the inertia of the whole Earth 
makes the precessional movement nearly uniform. The 

i, too, has its share in occasioning precession; but 
although the Sun's mass is vastly greater than the Moon's, 

s so far from the Earth that the difference of its distances 

n the nearer and farther sides of the Earth is trifling 
compared with either of these distances. Hence its effect 
than that of the Moon. Even the planets have some- 
thing to do with precession, but only because they draw the 

th out of its orbit, and so change the plane of the ecliptic ; 
the effect of this on precession is called planetary, preces- 
sion, while that of the change in the plane of the equator due 
to the Moon and Sun is called in part luni-solar precession, 
and in part nutation. 

The Moon has a precessional movement (181), from 

which it has been inferred that it is not a perfect sphere 

The other bodies of the Solar System may have 

similar movements ; but the directions of their axes are not 

. accurately known, and hence we cannot observe small 
changes in these directions. The satellites of Jupiter and 

:rn are always nearly in the planes of the equators of 

it planets, so that it is not likely that Jupiter and Saturn 
have much precessional movement, although they seem to 
be still less nearly spherical than the Earth. 

If a quantity of any kind of liquid is placed so far 
from other bodies that its separate parts may be considered 
as being all equally distant from an the 



34o Outlines of Astronomy. [Sec. 671. 

movements of its various parts with respect to each other 
will bring it, under the law of gravitation alone, into the 
shape of a sphere. But if a liquid sphere is near enough 
some other material object to make any noticeable difference 
in the distances of its separate parts from that object, it can 
no longer keep its spherical shape. For this difference in 
distance must make a difference in movement under the law 
of gravitation. If we suppose several objects all in a line 
with each other, one of which. /, Is farther from the othi 
A, B, C, etc., than they are from each other, it is plain that 
the movement towards each other of A. B, and C. must be 
less than it would be if there were no Z : since the nv 
ment of each of them towards Z is .small in pro] i the 

Square of its distance from Z. If the mass of / 
compared with the in the other bodies, they may be 

actually drawn apart from each other by the difference 
Speed in their movements toward Z : on the other hand, 
their movements towards each other may be sufficient to 
prevent them from being actually drawn apart. In either 
case, however, their places with respect to Z make a di:; 
ence in their movements, which is usually ( ! by 

Baying that their attraction for each other is lessened by Z. 

. The movements of the separate parts of a liquid 
sphere, undisturbed by other bodie linst 

each other by the law nf gravitation that each part remains 
at rest. But if this equilibrium, as it is called is disturbed 
by another body, the parts of the sphere must move with 
respect to each other until they have again come to equilib- 
rium in some new arrangement. This will change the 
sphere, in most cases, to a spheroid with one axis loi 
than any other ; and the long axis will point towards the 
disturbing body. We m v ^cneral notion of this | 

cess by considering the weight, though not the mass, of the 
parts of the sphere in a line with each other and with the 
disturbing body to be lessened. Under these circumstances 
the parts on each side will crowd in upon them, and the 
sphere wall be pushed out of shape. When this change has 



Sec. 672.] Theoretical Astronomy. 341 

gone far enough for the increased bulk of the spheroid, 
g the line pointing to the disturbing body, to make up 

for its diminished weight along this line, the equilibrium of 
irts will be restored. 

This consideration enables us to account for the fact 
that the Moon raises the tide on the side of the Earth from 
which it is farthest as well as on that which faces it. The 
solid parts of the Earth are not free to change their shape, 
but the ocean may have some movement with respect to the 
Moon like that of the outer parts of a liquid spheroid. The 
easiest way to understand the rise of the tide on opposite 
sides of the Earth at the same time is to regard the water as 
lightened more or less according to its distance from the line 
sing through the centres of the Moon and Earth, the 
ter along this line being lightened most. But where it is 
lightest it must also be deepest : that is, its surface must 
reach farther from the centre of the Earth than that of the 
heavier water on both sides of it, in order to balance the 
pressure of this heavy water. In like manner, the surface 
of the ocean near the equator always stands farther from the 
Earth's centre than the surface of the ocean near the poles 
(162). The Moon has little effect in lightening the ocean 
compared with the effect of the Earth's shape and rotation : 
for the level of the water at the equator differs from that of 
the polar oceans by about twenty-six miles, while the tides 
around islands in the open ocean only rise two or three feet. 
In narrow bays and in rivers, the various currents of water 
which are started by the tide sometimes make the sea rise 
much more than it does in the open ocean (278). 

As the Earth's rotation turns one part of it after 
another towards the Moon, the places where the tide is high- 
est at the time are steadily changed. Hence there are ordi- 
narily two high tides every day : but the day. if measured by 
the Moon, is longer than a flay of mean time (340). The move- 
ments of the ocean which occasion the tides must obviously 
be altered by the inertia due to the Earth's rotation : so that 
even if the Earth were wholly liquid, or wholly covered with 



342 Outlines of Astronomy. [Sec. 674. 

water, it would not follow that the two places where the water, 
at any given time, was deepest, would be those nearest the 
Moon and farthest from it. Moreover, the distribution of 
land and water on the Earth's surface makes the actual tides 
of any place dependent on various tidal waves and currents; 
so that the time of high tide is not often very near the time 
of the Moon's culmination, but usually comes a certain num- 
ber of hours later. Along the eastern coast of New England, 
for instance, the time of high tide is about eleven and one- 
third hours after the Moon's culmination, so that it happens 
little more than an hour before the next culmination of the 
Moon (340). Other irregularities in the tides, some of which 
are curious enough, are due to the fact that the irbit 

takes it sometimes north and sometimes south of the plane 
of the equator. This fact would naturally make a difference 
in the height of the two daily tides. When the Moon is 
north of the equator, for instance, we should expect the high 
tide due to its upper culmination' to be higher in the northern 
hemisphere, and lower in the southern, than the high tide 
due to its lower culmination. This difference sometil 
actually appears ; but in many places it is made up for by 
the manner in which the tidal wav< mbined with each 

other by the form of the coasts along which they sweep. 
A wave, as every one may observe for himself, may move 
quickly while the particular portions of water which form it 
at any one time are carried up and down, or forward and 
back, only a little ; since the water which makes up the w 
is constantly changing as the wav< >n. At the same 

time, when the wave is broad, like a tidal wave, however low 
it may be, it may give rise to strong currents, particularly in 
shallow water. On the coast of New England, each of the 
two daily tides is about as high as the other ; while on the 
coast of California, one of them is usually large and the other 
small. 

675. The reason why the Moon has so much more than 
any other celestial body to do with the tides is the same 
which accounts for its comparatively great effect in occasion- 



Sec. 675.] Theoretical Astronomy. 343 

ing precession (669). But the tides clue to the Sun are 
,e enough to be readily noticed ; hence when the Sun and 
m are in conjunction or opposition, so that their effects 
are combined, the tides rise highest. This happens, of 
course, when the Moon is new or full. Since the tides 
the eastern coast of New England are about eleven hours 
late (674), the eleven o'clock tide is the highest on that coast, 
ut the time of half moon, the tides rise and fall compara- 
tively little ; they are sometimes called neap tides, while those 
which occur when the Moon is new or full are called spring 
tides. 

676. The Moon's varying distance from the Earth makes 
a difference in the amount of the tides ; a spring tide occur- 
ring when the Moon is in perigee will be unusually high. 



344 Outlines of Astronomy. . 677. 



CHAPTER XV. 

HISTORY OF AS MY. 

677. At the present clay, the progress of astronomical 
knowledge depends Oil ingenious instruments, accurate m< 
lirementS, and intricate calculations. No one can obtain 
the means of forming an opinion of his own upon astro- 
nomical questions until he has fitted himself to cons 
them by learning how to use strict mathematical forms 
reasoning, and how to apply his reasoning to actual observa- 
tions. Most of us, who cannot spare time for the thorough 
study of astronomy, must be content to take for granted the 

correctness of any opinion generally held by edu< tron- 

omers on the subjects of their science ; hut we need not at 
once accept every new .statement announced as an astronom- 
ical discovery, for many such statements prove to be I 
takes. There is no way of preventing mistakes altogether, 
even among men who are distinguished in science. In I 
if the full history of astronomy, or of any other branch of 
knowledge, were recorded, we should find it I >t mainly 

of an account of mistakes. As it is sometimes written, how- 
ever, it gives us the impression that the ancient astronomers 
did little but make mistakes, and that modern astronomer- 
little but discover truths. But this impression is s< arcely fair. 
In our own times, many careless guesses are put forward as 
if they were part of science, just as similar put 

forward long ago. Indeed, people who have not learned 
astronomy sometimes undertake to speculate about astro- 
nomical subjects, and so waste a great deal of time in a way 
which is much more foolish than it would have been hundreds 
of years ago, when nothing was definitely known about any 
of the natural sciences. On the other hand, we find that in 
past ages, as well as in recent times, there have been men 



Sec. 677.] History of Astronomy. 345 

who attentively observed the facts of nature, and tried to 

. reasonable judgments about the tacts which they had 

ierved. Even the mistakes of men of this kind are more 

i table to them than any mere fancies could have been, 

admitting these fancies to have been correct. 

678. Among the most remarkable fancies of mankind with 
rd to the stars was that from which arose the study of 

astrology. There is little difference in the original meaning 
of the words astrology and astronomy, and they were once 
both used to mean the study of the various celestial objects. 
For the past three centuries, however, and perhaps longer, 
astrology has been generally understood to mean only the 
mpt to foretell the course of human affairs by calcu- 
lations founded on certain real or imaginary astronomical 
observations. No one who wishes to be considered sensible 
now pretends to think that this can be done ; but in past 
times a great deal of study and ingenuity were laid out in 
drawing up rules for astrological inquiries. 

679. The first astronomers of whose observations and 
theories we have any distinct account lived in the various 
Grecian settlements on the coast and on the islands of the 
Mediterranean Sea. Some attention seems to have been 
paid to astronomy in still more ancient times by the Egyptians 
and Chaldeans, and also in Hindostan and China: but little 

known to have been learned by any early astronomers 
ept the Greeks. We find in several of the Egyptian pyr- 
amids slanting passages leading downwards into the pyra- 
mids from their northern faces. The slant of these pass 

ich that the part of the sky seen by an observer at the 

<_*r end of one of them is about 4 below the north pol 

the celestial sphere. These pyramids are supposed to have 

n built about four thousand years ago and at that time 

rather I within 4 of the | 

that it could be seen from the p just mentioned at 

r culmination. It is probable that the slant of the 

signed to permit 1 of this kind, 

although the u.^e made of thi I known. 



346 Outlines of Astronomy. [Sec. 679. 

To make a fair estimate of the attainments of the early 
astronomers, and especially of the Grecian astronoi 

must notice how little is known about the stars by m 
people at the present (lay. and what astronomical facts can 
now he observed without the help of expensive instrumc 
While scarcely any one now knows any thing of these facts 
except what he has learned about them from 1>< -t of 

them have been familiar to astronomers for the last two 
thousand years, and probably still longer ; so that there must 
have been much interest in actual observation in very early 
times, although doubtless than there n< iong 

scientific men. since its usefulm ly shown. 

680. The first step in astronomy for an observer who 

no instruments must consist in learnii . con* 

siderable number of the bright stars. This may be done 
with a little patience by any one. even if he has no ma; 
globe to tell him the names of tin It is all very well 

to know the name by which other people call some par: 
lar star: but after all. the know: 

ird to that star « (insists in his being able to distinguish it 
from others ; and he can give it a name of his own, if he 
likes, which will serve this purpose .is well 
name, so far as he is con< erned ; although when he has any 
thing to say about it to other people, he must use a name 
it which they will understand. 

681. The method of nami used among the Greeks 
was too cumbrous to be of any service in our times. The 
stars were arranged in fanciful groups, each supposed to 
represent the figure of some animate or inanimate 

and any particular star was named by its place in the figure 
to which it belonged (82). Siriiis, however, and a f< 
stars, had names oi their own. In later times many of the 
stars had special names among the Arabian astronomers, 
which are still sometimes used, although they have 1 1 
oddly altered in their passage from the Arabic into Europe 
languages. 

682. The groups, or constellations, in which the ancient 



Sec. 682.] History of Astronomy. 347 

astronomers considered the stars as arranged, probably had 
rst no exact boundaries. Claudius Ptolemaeus, or Ptol- 
emy, as he is usually called, drew up the first list of fixed 
rs which has come down to our times. This astronomer 
lived at Alexandria in Egypt, about A.D. 140. On the svs- 
he employed, no star was regarded as belonging to a 
stellation unless it was within the boundaries of a figure 
representing- that constellation, and distinct from other fig- 
ures. The names of Ptolemy's constellations are still in the 
main retained ; but according to Ptolemy's arrangement 
there were many stars which did not lie within the boun- 
daries of any constellation. Later astronomers extended the 
limits of the constellations, and formed several new ones, so 
that every star might be within the boundaries of some con- 
stellation. By this change, a constellation came to mean 
merely a portion of the sky, and could no longer be consid- 
ered as a figure formed by a group of stars. 

Xo improvement was made in the method of naming 

rs till a.d. 1603. when a set of maps of the constellations 

3 published by Bayer, a German. In these maps the 

stars of each constellation were distinguished from each 

other by letters, the first letters of the Greek alphabet being 

^ned to the brightest stars. This convenient practice is 

still in use. 

>ut a century later. Flamsteed, an English astron- 
omer, made a catalogue of stars in which the stars of each 
constellation were arranged in the order of their right ascen- 
sion at the time of the catalogue. Flamsteed also arranged 
in the order of right ascension the stars of each constellation 
found in the catalogue of Hevelius (a German astronomer 
of about the same time;, as well as those found in some 
earlier catalogues. 

In our day, stars are not catalogued according to 
r constellations, but are arranged in order of right ascen- 
throughout ; and each stir is distinguished from the 
• merely by a statement of its right ascension and declina- 
tion at some particular date. However, many stars arc still 






348 Outlines of Astronomy. [Sec. 685. 

referred to in speech or writing by their names, letters, or 
numbers. When letters, or numbers showing the order of 
the stars in Flamsteed's catalogue, and that of Hevelius as 
arranged by Flamsteed, are used as names of star 
names of the constellations have to be added. The names 
of the constellations used by astronomers who write in Eng- 
lish are Latin words answering in most cases to the Greek 
names found in Ptolemy's catalogue. Thus a Tauri means 
the star Alpha of the constellation Taurus, also called Al- 
debaran ; a Canis Major is, or Alpha of the constellation 
Canis Major, is Sirius ; 1 Pegasi means the first star of the 
constellation Pegasus in Flamsteed's catalogue: 51 Cephei 
(H.) means the fifty- first star of the constellation Cepheus 
from the catalogue of Hevelius arranged by Flamsteed. 
Stars may likewise be referred to by their numbers in mod- 
ern catalogues ; in that case the names of the constellations 
are not needed. 

686. After learning to distinguish one star from another, 
an observer will be able to compare the brightness of each 
star he knows with that of any other. In the absence of any 
accurate photometers, such as are now used for this pui 

all that can be done is to classify the stars according to 
their brightness. The comparative brightness of the stars 
of Ptolemy's catalogue is expressed by what Ptolemy, and 
other astronomers after him. have called magnitude (81); 
each star being said to be of the first, second, third, fourth, 
fifth, or sixth magnitude. Since the invention of teh 
many additional magnitudes are recognized. 

687. The periodical changes of brightness in certain stars 
(98) seem to have escaped the observation of all the ancient 
astronomers. Fabricius. a Dutch astronomer, was the first 
to discover the variability of Mira, or o Ceti : and this 1 
covery was not made till 1596. But now that stars are 
known to vary, no instruments are needed to show the 
changes of brightness in Mira, Algol, and a few other stars. 

688. In making measurements of the apparent places of 
the stars, the Greek astronomers followed the method which 



G. 6SS.] History of Astronomy. 349 

g come down to us from them. They measured distances 
stial sphere in fractions of great circles, dividing 
h circle into degrees and minutes of arc. Every one, 
11 if he has no instruments, should accustom himself thus 
the apparent distances between stars, instead of 
of length, as many people do, to express 
quantities which are really angles. The number of degrees 
in the angle or arc between two stars can be roughly deter- 
mined by estimating the number of times that the arc would 
be contained in the circle of the horizon, which contains 360°, 
or in the upper 1S0 of any vertical circle, the meridian, for 
• ince. If a celestial atlas or globe is at hand, the arc of 
a meridian between any two stars which have about the same 
: ascension can be learned at once ; and when these 
in be recognized in the sky, the arc between them 
will serve as a standard for other estimates. Care must be 
en to distinguish between great and small circles, and all 
measurements are to be made in fractions of a great circle 
People without mathematical knowledge used in 
ancient times to talk of the Sun as a foot (for instance) in 
diameter, just as people like them do now-a-days. But the 
educated Grecian astronomers perfectly understood that the 
apparent diameter of the Sun, or of any object, is an angle 
and not a distance. 

689. The diurnal movement (524) is the only one in which 
all the celestial objects take part. It may easily be observed 

out instruments, as we have seen (124), and every edtl- 

d person should have got some practical knowledge of it. 

He should notice, for instance, if he lives in the northern 

hemisphere of the Earth, what fraction of the meridian is 

included between the north point of the horizon and the 

5l ir. lb- should know the course of the equator on 

the re, not merely from maps, but from his own 

rvations. 

690. The explanation of the diurnal mi 

.mong the ancients was that of t! 
already mentioned (126, 128). Put the explanation of the 



3So Outlines of Astronomy. [Sec. 690. 

same facts by the rotation of the Earth was also undertaken 
much more than two thousand yens ago. Neither of these 
explanations could then be shown to be correct ; and 
astronomers who maintained the view which is n 
erally accepted do not seem to have taken much trouble to 
contrive observations or experiments by which their theory 
could be tested. Little credit, therefore, can be given them 
for the accidental correctness of their gues>- 

691. To show that the Sun is constantly lagging behind 
the other stars in their diurnal movement (322), it was only 
necessary to watch the rising and setting of different stars at 
dilTerent seasons of the year. These appearani 
perceived to return yearly in the same order, and the predic- 
tion of them was considered an important part of astronomy, 
until astronomers learned to make more difficult and more 
valuable predictions. At some rather late period in the his- 
tory of astronomy, which cannot, perhaps, be exactly deter- 
mined, the names of heliacal, cosmical, and acronycal ris 
and setting came into use instead of longer names applied to 
like facts by the ancient astronomers. A star rises heliacally 
when it rises only just soon enough to be seen before sum 
and sets heliacally when it s< >on after sunset that 
it can barely be seen. Its cosmical rising happens when it 
rises exactly at the same time with the Sun, and when it 
rises just at sunset, the rising is acronycal. A star may set 
just at sunrise or just at sunset, but authorities differ as to 
which of these settings should be called cosmical. and which 
acronycal. 

692. The ancient poets frecpiently mention the rising and 
setting of certain constellations without stating what kind of 
rising and setting thev mean. It is only on this account that 
the preceding explanation is worth giving. The days of the 
heliacal setting and the acronycal rising of a star are likely in 
practice to be more frequently spoken of than the days of the 
other appearances above mentioned ; since this setting and 
this rising happen early in the evening, when the stars are 
usually most noticed. The acronycal rising cannot be directly 



Sec. 692.] History of Astronomy. 351 

seen ; but any star seen near the eastern horizon as soon as 
' irk may be supposed to have risen about sunset. 

693. Close observation of the heliacal settings and risings 
3 apparently near the Sun will enable any one to trace 

out the Sun's course among the stars ; and this had been 
e, no doubt, before the time of the earliest astronomical 
ords. It had been noticed, too, that the Sun pursued the 
same course year alter year, so far as could be shown by rude 
nations. The belt of the sky marked out by the con- 
stellations through which this course passed was called the 
zodiac ; the course itself was recognized as a great circle of 
the celestial sphere, and the angle between its plane and that 
of the equator was pretty well determined. One common 
name for the Sun's course was the oblique circle, to distin- 
sh it from the equator, the plane of which is perpendicular 
to the axis of the diurnal movement. In later times, the 
oblique circle got its present name of ecliptic from the cir- 
cumstance that eclipses can happen only when the Moon 
is near the ecliptic. The width of the zodiac was set down 
as just 12 by some ancient astronomers. The ecliptic was 
divided into twelve arcs each of 30 ; these arcs were named 
after the twelve zodiacal constellations, and were afterwards 
called signs. These signs never corresponded to the con- 
stellations after which they were named, for some of the 
constellations take in more than 30 of longitude, and others 
less. Besides this, precession is always shifting the longitude 
of a constellation ; while the sign Aries, for example, always 
took in the first 30 of the ecliptic, counting from the vernal 
, equinox. Modern astronomers have left off the practice of 
dividing the ecliptic into signs. 

694. It is by no means a modern notion that the apparent 
movement of the Sun in the ecliptic is due to a yearly move- 
ment of the Earth round the Sun. Aristan bus of Samos, 

vrer 2,100 years ago, certainly proposed this expla- 
' nation, and answered the chief objection to it by th< 

ns that the stars were so fir from the Sun and Earth that 
no apparent change in their places could be occasioned by 



352 Outlines of Astronomy. [Sec. 694. 

the Earth's movements round the Sun. It shows how little 
can be done in science by guesswork alone, that the opinions 
of Aristarchus were not accepted by Liter astronom 
were almost wholly forgotten for some eighteen hundi\ 
If Aristarchus had found out any system of calculi 
means of which the apparent places of the plai I be 

readily foretold according to his theory, no educated astrono- 
mer would have afterwards considered the 'ion- 
ary. But it was not till about two hundred years later that 
Hipparchus succeeded in inventii tern of calculation 
by which predictions could be made much more correctly 
than had been practicable before his time. Hipparchus, 
who lived at Rh »re the Christian 
era, seems to have invented instruments, as well as calcu- 
lations, of new kinds, and to have been industrious in the 
of all his inventions. IK- was the first. is know: 
make a catalogue of stars. Ptolemy's catalogue, indeei 
supposed to be merely a copy of that made by Hipparchus, 
altered enough to allow for what Ptolemy suppoi e the 
amount of | I a since the date of the catalogue he 
copied. The fact of] n was known to Hipparchus as 
well as to Ptolemy; but even in Ptolemy's time, its amount 
had not been ascertained. Apparently Ptolemy might have 
done something to determine it if he had made more obser- 
vations of his own and had compared his results carefully 
With those of Hipparchus. For want of this, his catalogue is 
not nearly correct for his own time. 

695. The system of calculation employed by Hipparchus 
and his successors was founded on what we call trigonometry, 
a branch of mathematics which Hipparchus seems to have 
been the first to discover. His method, as might be expected, 
was clumsy, but it served its purpose. The theory to which 
it was applied seems not to have originated with Hipparchu>, 
who adopted it from some of his predecessors. In this 
theory, the Earth was regarded as stationary, and the m< 
ments of celestial objects were resolved into circular move- 
ments variously combined. It was adopted and developed by 



Sec. 695.] History of Astronomy. 353 

Ptolemy, and continued in use among astronomers until about 
two hundred and fifty years ago. When it is now mentioned, 
it is usually called the theory of epicycles. Connected with 
this theory were many suppositions about solid transparent 
spheres (like the sphere of the fixed stars) revolving within 
each other; but these suppositions, which were older than 
the time of Hipparchus, have in fact little to do with his 
n, which consisted in the mathematical combination of 
rent movements. 

696. It was probably unfortunate that Hipparchus did not 
apply his mathematical inventions to the theory of Aris- 
Urchus ; but this mistake has not prevented him from being 

ered in modern times as the founder of the science of 
astronomy. His merit consisted not in guesswork, but in 
actual observation and in the invention of methods by which 

ations could be made available for predictions. These 
methods, indeed, furnished the means by which the defects 
of the theory of epicycles were at length made to appear. 

697. Aristarchus himself seems to have been a good mathe- 
matician for the time at which he lived, and his actual obser- 
vations and calculations were more valuable than the correct 
suppositions which he made without discovering the means 

ing them. Hipparchus did so much to provide these 
means that the incorrectness of his theories was of compara- 
y little consequence. 

698. Although the Earth might in ancient times be reason- 
ought to be at rest, its globular shape could not be 

ted by any attentive observer. The opinion prevalent 
arnon^ the Greek astronomers, indeed, seems to have been 
that the Earth is a sphere ; and in later times, even when the 
»ed political condition of Europe had produced the de- 
cline of civilization which for some centuries almost wholly 
checked the progress of natural science, many intelligent and 
educated men were aware that the Earth could not be flat. 
Any one who has occasion to travel a few hundred miles 
northward or southward, and who closely watches the stars 
during bis journey, may see for himself that either the verti- 
go 



354 Outlines of Astronomy. [Sec. 698. 

cal lines of the different places he travels through have dif- 
ferent directions, or else the stars are so near that he actually 
passes by some of them on his way. But in this last ca 
if we travel northward, the southern stars ought to seem 
closer together than before ; and if we travel southward, they 
ought to appear to spread apart, while the northern si 
should draw together. In fact, however, we cannot prod 
any apparent movements of the stars among each other by 
our journeys on the Earth. Hence it no doubt became man- 
ifest in early times to careful observers that the stars m 
be at least so far away from the Earth as to make the lines I 
drawn to any star from different terrestrial places too nearly! 
parallel with each other to be distinguished from strictly par- 1 
allel lines. Then, since the stars which daily pass near thel 
zenith of one terrestrial place are not the same with those I 
which daily pass near the zenith of a place some distance I 
north or south of it, we are forced to conclude that thel 
zeniths of the two places are in different directions fronrl 
the Earth. Now this amount ng that the Earth h 

globular; for its surface seems on the whole to be every- J 
where horizontal, while yet any two places on that surfactl 
differ in their horizontal planes, as they must if the direction!! 
of their vertical lines are different. We see, too, that as w«| 
travel northward or southward the place of the zenith moveJ 
with us, not the contrary way, .is it would if the Earth's sur- 
face were hollowed out, or cup-shaped. YVe conclude, then,! 
that it is everywhere globular, or at all events rounded of ji 
northwards and southwards. Although the diurnal motion! 
of the stars makes it less easy to show directly that the Eart \ 
is rounded eastwards and westwards also, the very facts | 
this diurnal motion make it likely that such is the case. 11 
is not surprising, then, that the ancient astronomers 
pretty correct notion of the shape of the Earth ; but thi*J 
notion of theirs shows that they were better observers than 
many educated people of modern times. 

699. The size of the Earth, admitting it to be a splnr* 
can be judged of roughly by noticing how much travel! n; 



6Q9-] History of Astronomy. 355 

northward or southward is required to shift the place of the 

th i°; the simplest way of doing this is serve the 

£ths of shadows at noon on the same day in two places 

nearly on the same meridian. The Greek astronomers had 

in fact obtained in this manner fair estimates of the length 

of a diameter ot the Earth, but as they had no means 

making accurate surveys ot* its surface, they were never able 

more than merely estimate this length. 

700. Even in our time it is difficult to determine the dis- 
tance of the Earth from other bodies, and it is not wonder- 
ful that the ancient astronomers had little success in their 
attempts to find the distance of the Sun. They learned, 

ever, to regard the Sun as at least so far from the Earth, 
that in order to have its apparent diameter of about half a 

oee, its actual diameter must be several times longer than 
that of the Earth. To show this, they had only to compare 
the places of the ecliptic among the stars which result from 

nervations made in different terrestrial places. As there 
is no noticeable difference between these places of the eclip- 
:t follows that if the stars could be seen in the daytime, 
the Sun, as viewed at the same time by observers in different 
parts of the Earth, would seem to all the observers in the 
same place among the stars. Hence, if the Sun is nearer 
than the stars, it must at all events be far away compared 
with the distance between any two terrestrial places. This 
may have made the theory of Aristarchus seem very unlikely 
to his successors ; for if the Sun was allowed to be so dis- 
tant that it showed no parallax with respect to the stars, it 
would certainly seem strange that the yearly motion of the 

rth round the Sun could take place without changing the 
apparent places of the stars with respect to each other. 

701. Aristarchus tried to determine the comparative 
tance of the Sun and Moon from the Earth by r< 
from their apparent places at the moment of half nv 
when the lines from the Moon to the Sun and to the Earth 
must be perpendicular to each ot! lie could n< ither 
observe the time of half moon nor the place Mm and 



356 Outlines of Astronomy. [Sec. 701. 

Moon with the precision required to make this method useful. 
However, he supposed himself to have made his observations 
accurately enough to warrant the conclusion that the Sun \ 
from eighteen to twenty times as far away as the Moon. 

702. The distance of the Moon could be most satisfacto- 
rily determined in ancient times by the comparison of obser- 
vations of some eclipse of the Sun as seen from different 
places. It must soon have been noticed that no eclipse of 
the Sun was total in all terrestrial places ; and that some dis- 
tance north of the place where an eclipse appears total, the 
northern part of the Sun is seen beyond the Moon, while 
the southern part is visible at places far to the south. Hip- 
parchus was enabled, by his improvements in mathem.it 
to calculate the Moon's distance from the observations made 
at Alexandria and on the Hellespont ol a remarkable solar 
eclipse. The observations were not precise enough to give a 

result very close to the truth, except by accident; but Hip- 
parchus concluded that assuming the Sun's par.dlax to be 
small, the distance of the Moon was about seventy seven 
times the semidiameter, or radius, of the Earth (sixty times 
would have been nearer right, and in fact other determina- 
tions attributed to Ilipparchus range from about sixty to 
about eighty). Ptolemy proposed a method of finding the 
Moon's parallax by observing its zenith distance at the time 
of its culmination, and comparing this observed zenith dis- 
tance with the zenith distance calculated for the time of the 
observation from the observer's latitude and the supposed 
orbit of the Moon. The instrument contrived for the obser- 
vation consisted of an upright standard, carrying a movable 
arm with sights through which the Moon was observed. 
The uprightness of the standard was tested by a plumb-line 
hung beside it. The angle formed by the standard and the 
arm, which were of equal length, was measured by divisions 
on a second arm jointed to the lower end of the standard. 
This instrument could not give precise results, and the facts 
required for the calculation of the Moon's geocentric place 
were ill-determined in Ptolemy's time. Hence his conclu- 



Sec. 702.] History of Astronomy. 357 

sions are untrustworthy, although the result he reports is not 
far wrong ; but both Hipparchus and Ptolemy supposed the 
distance between the Earth and Moon to vary much more 
than it really does. Instruments of the kind just mentioned 
were sometimes used by later astronomers. They were called 
parallactic rules, and also k * Ptolemy's rules." Modern as- 
tronomers imitate Ptolemy in determining parallax from zenith 
distances observed on the meridian; but when the Moon's 
parallax is thus to be determined, numerous observations are 
made at each of two places far distant from each other. 

703. Another instrument used by Ptolemy, and probably 
invented by Hipparchus, was the astrolabe, a combination 
of graduated circles provided with sights, which was mainly 
used in measuring celestial latitudes and longitudes. The 
name of astrolabe has also been applied to a simpler instru- 
ment used in taking altitudes. 

704. The best ancient time-keepers were water-clocks. 
These are vessels out of which, or into which, water is 
allowed to leak through small openings. Water-clocks of 
the first kind are usually called clepsydras ; they were used 
extensively by the Greeks and Romans. Water-clocks of 
the second kind were used in Hindostan. By the time re- 
quired to empty or fill the vessel, as the case may be, the day 
may be measured off into parts of about equal length. 

705. An upright pillar, or gnomon, was anciently an astro- 
nomical instrument of some value. It showed the compara- 
tive length of the shortest shadows on different days in the 

r ; and in this way the length of the tropical year itself, 
and the differences of latitude of different places, could be 
tolerably well made out (699). 

706. Little progress was made in any of the natural sci- 
ences for nearly fourteen hundred years after Ptolemy's 
time. For several centuries after the great conquests of 
the Arabs and the other Mahometan nations, there was more 
scientific study among them than anywhere else ; but al- 
though many of their astronomers showed some talent, they 
made little improvement in the astronomy of the Greeks. 



3s3 Outlines of Astronomy. [Sec. 706. 

Their recorded observations have at times been serviceable to 
modern astronomers, and they did something to improve the 
methods of calculation invented by Hipparchus and Ptolemy. 

707. From time to time, attempts were made to correct the 
suppositions on which astronomical predictions were four 
These suppositions related to the extent and rate of the vari- 
ous circular motions into which those of celestial objects were 
resolved ; and their chief results drawn up in systematic form, 
so as to be useful in computation, woe called tables. The 
first astrononomical tables which seem to have been drawn 
up in Europe were those called the Alphonsine Tables, after 
Alphonso X. of Castile, who employed the best astronon. 
of his time in their construction. Alphonso reigned in the 
last half of the thirteenth century. 

708. About two hundred years later, the German astrono- 
mer Regiomontanus undertook the construction of a calendar 
containing astronomical predictions for several years to come. 
Calendars, in this sense of the word, or ephemeri they 
are now frequently called, differ from tables in giving the pre- 
dictions of particular events which can be observed, while 
tables give the materials for the construction of predictio 
The predictions of Regiomontanus g the 
faulty theory on which they were founded ; but the time had 
now come for this theory to be questioned 

709. Copernicus, who lived in the first half of the sixteenth 
century, reinvented and extended the theory of Arist ar- 
chus. By regarding all the planets, including the Earth, 
as revolving about the Sun, while he considered the Moon as 
accompanying the Earth in its revolution, and at the same 
time revolving about it, he materially simplified the theory of 
astronomy. The phenomena of precession were also 1 
plained on right principles by Copernicus. He did tiot 
succeed, however, in removing the difficulties of the old 
system of astronomy : for he supposed the orbits of the 
planets to be circular, and was therefore obliged, like the 
ancients, to account for the results of observation by com- 
plicated combinations of circular movements. 



Sec. 710.] History of Astronomy. 359 

710. Towards the end of the same century, Tvcho Brahe* 
long and accurate scries of astronomical observations 

on an island near Copenhagen. His reputation as an astron- 
omer depends on these observations ; his theories were not 
important. But his observations furnished the means by 
which an astronomical discovery, more important than any 
which had been made since the time of Hipparchus, was to 
be brought about. Tvcho Brahe was obliged, towards the 
close of his life, to withdraw from Denmark, in consequence 
of the ill-will of persons of influence at the Danish court. He 
removed to Prague, where he became acquainted with Kepler. 

711. The recorded observations of Tycho Brahc enabled 
K.pler to discover his three celebrated laws. This discovery 

- no mere guess ; although Kepler made many fanciful 
-ses, he was ready and able to test "his guesses by the 
difficult calculations required for the purpose of comparing 
their results with those of actual observation ; and when he 
found that either a guess or an observation must be wrong, he 
did not insist, like many fanciful people, that the error lay 
in the observation. His theory, when it was finally made 
out, enabled him successfully to represent the apparent move- 
ments of Mars (the planet to which his work was mainly 
confined) by two elliptical movements, one attributed to the 
Earth and the other to Mars ; the speed of these movements 
being determined by the law that the radius vector of each 
planet passed over equal areas in equal times. This dis- 
covery put an end to the need of attributing various circular 
movements to a single planet. 

712. The value of Kepler's work lay in what he proved, not 
in what he conjectured. If his guesses had been valuable in 
themselves, he would be considered one of the chief invent 

of the laws of motion now accepted, including the law of 

gravitation. He supposed that material 1 

each other, but he could not show exactly 1 

each other. His really important dis< 

once recognized among the numei illations 

with which he had filled his writings ; and in his own time 



360 Outlines of Astronomy. [Sec. 712. 

the great improvement which he had made in the theory of 
Copernicus seems to have passed unnoticed. 

713. Besides discovering the laws of planetary motion, 
Kepler also took part in the great discovery of the tele- 
scope, which was made in his times. He seems to have 
been the first to describe that combination of two convex 
lenses the principle of which is now in universal use in 
astronomical instruments. He also improved the theory of 
astronomical refraction. 

714.. In a treatise on optics, by Ptolemy, the fact of refrac- 
tion by the air is noticed and explained on right principles. 
The fact, too, that the eclipsed Moon may sometimes be seen 
in the east before sunset was noticed in ancient times, and 
its explanation by the theory- of refraction was attempted. 
Still, the Greek astronomers never learned much about 
refraction. The Arabic astronomers studied it to some 
extent, and Tycho Brahd, as well as other astronomers, had 
also attended to its effects. Kepler drew up empirical rules 
for calculating refraction, which gave nearly correct results, 
except close to the horizon, where even the rules of modern 
astronomers are often at fault, on account of the great vari- 
ations in the state of the lower parts of the Earth's atmos- 
phere. 

715. The work in which Kepler stated his first and second 
laws of planetary motion appeared in 1609 : he stated his 
third law in a work published ten years later. Some writers 
prefer to arrange these laws in one order, some in another ; 
the arrangement given above (150) seems on the whole most 
conformable to the course of Kepler's reasonings, although 
the general principle of the second law seems to have oc- 
curred to him before he had assigned elliptic orbits to the 
planets. 

716. We may consider the rapid progress of physical 
science, which forms one of the most noticeable parts of 
modern history, to have begun about the time at which 
Kepler lived. The number of men who did valuable work 
in science became so large during die seventeenth century 



Sec. 716.] History of Astronomy. 361 

that it is impossible in any short account of the progress o{ 
astronomy to name more than a few even of those who at- 
ed the most important astronomical results. Galileo, a 
celebrated Italian, contemporary with Kepler, by his experi- 
ments in mechanics, greatly assisted in the discovery of our 

sent laws of motion. He was the first, also, to make 

ronomical discoveries by means of the telescope. Having 
heard, in 1609. of the accidental invention of magnifying instru- 
ments in Holland, he found little difficulty in discovering, on 
known principles of optics and geometry, one of the plans on 

ich telescopes may be constructed. This plan is that 
on which each of the telescopes of an opera-glass is now- 
made ; it is not in use in astronomical telescopes. Galileo 
overed the satellites of Jupiter and observed spots on the 

1 with telescopes of his own construction ; he also saw 
that there were projections on each side of Saturn, but his 
instrument did not show the ring distinctly. 

717 Huygens, about fifty years later, made considerable 
improvements in telescopes and in clocks. No achromatic 

-cope had yet been made, and in order to obtain more 

^ai tying power than that of former telescopes, without 
blurring the image. Huygens had to use object-glasses of 

iter focal length than is now given even to the largest 
Some of his telescopes had no tubes, their object- 
ses being mounted separately from their eye-pieo 

ygens was born at Amsterdam, but passed much time 
in France and England. He discovered the ring of Saturn 
and one of its satellites, and observed the rotation of Mars. 
Picard, a French contemporary of Huygens com- 
bined the telescope with graduated arcs for making measure- 
ments in the modern manner. In 1670 he determined the 

rth's diameter far more exactly than had been previously 

ie. For this purpose, he carefully measured line 

near Paris, from which he surveyed the country between 

rdon. near Amiens, and Malvoisine. near Paris; t! 
were his two astronomical stations. II' 
zenith distance at each station of a star in the constellation 



362 Outlines of Astronomy. [Sec. 718. 

Cassiopeia. The difference of these zenith distances, each of 
which was found by a great number of observations, gave 
him the angle formed by the vertical lines drawn in the plane 
of a meridian from two points, one in the latitude of Sour- 
don, and the other in that of Malvoisine. His sun 
him the distance along a meridian between these points. 
This distance was the length of that fraction of the whole 
meridian which was contained in the circumference of the 
Earth as many times as the angle to which it had been found 
to answer was contained in 360 . 

719. Four or five years before Picard's measurements, 
the celebrated English philosopher, Newton, had correctly 
guessed the law of gravitation : that is. he had conjectured, 
not that bodies attract each other, which was an old gu 
but according to what rule they move towards each other. 
But he had not published his guess, and given it out a 
great discovery. He had set himself to calculating how 
quickly the .Moon ought, under this rule and the law of iner- 
tia, to move round the Earth. The number of times which 
the Earth's diameter was contained in the Moon's distance 
had by this time been tolerably well settled, so that Newton 
knew pretty nearly the length of its orbit with respect to the 
Earth. But he employed in his calculations an estimate of 
the Earth's diameter which happened to be considerably too 
small. Hence, in his calculations, the Moon seemed to 
move slower than it really does, or that it should according 
to the law at which Newton had guessed ; for as he sup- 
posed the Moon's distance from the Earth to be less than it 
is. the number of miles it travels monthly with respect to the 
Earth is greater than he supposed. If Newton had been a 
practical astronomer, this would have set him to measuring 
the Earth. But he had many scientific occupations besides 
his inquiry into the Moon's movements, and he was not an 
astronomer by profession. Under like circumstances, many 
men would have published their guesses and calculations in 
order to claim the discovery of the law of gravitation if the 
Earth's diameter turned out afterwards to be longer than had 



Sec. 719.] History of Astronomy. 3G3 

been supposed. Newton simply put the inquiry aside and 

turned his attention to other matters. 

The results of Picard's survey and latitude observa- 
n to have attracted Newton's attention. lie 
was apparently led to resume his inquiries concerning the 
law of gravitation by the progress o\ similar inquiries among 
Other philosophers. One of his contemporaries, Dr. Hooke, 
had proposed a theor\ oi gravitation in 1O74: and in 1 
Hooke I that if the force of gravitation was in- 

proportional to the square of the distance between 
two bodies on which it acted, one body would circulate in an 
ellipse about the other. We see, then, that Hooke had 
guessed the law of gravitation itself. But he either could 
prove his guess for want of mathematical power, or at 
all events he neglected to prove it. 

Admitting the law of gravitation to be true, it was 
sy enough to show, as has been shown above, that it would 
account for Kepler's second law. and also for his third law, 
on the supposition that the orbits of the planets were circu- 
lar. But the science of mathematics was not yet sufficiently 
developed to permit Kepler's first law to be readily recon- 
ciled with the other two under the law of gravitation. This 
is the problem which could be solved only by the genius of 
wton. The greatness of his discovery consisted not in 
guessing the law of gravitation, for that could be done br- 
others but in proving what the consequences of such a law 

It seems that about the year 1679 he found out how 
to prove that two bodies moving under the laws of gravita- 
1 and of inertia, might circulate about each other in ellip- 
its. But then, being still unaware, perhaps, "f the 
Picard's work, he again dropped the sul 
* that we owe the completion of his work only in him, 

' and in part also to the 
This discoverer was the English astronomer i : 

-.ton Hooke, and other philosophers of his had 

been looking neral rules which would account 



364 Outlines of Astronomy. [Sec. 722. 

Kepler's laws. He had discussed the subject with Hooke, 
and as Hooke could not or did not show how elliptic move- 
ments might follow from the law of gravitation, H alley vis- 
ited Newton, whom he knew to be a distinguished mathe- 
matician, and asked him what he thought would be the path 
of a body moving about another under a law like that of 
gravitation. Newton replied that he had proved that this 
path might be elliptic. Halley recognized the importance of 
the discovery, urged Newton to complete his work, and took 
the expense of its publication upon himself. 

723. Newton's Principia appeared in 16S7, three years 
after the above-mentioned visit of Halley. The general 
laws of motion laid down in the Principia were before long 
almost universally accepted, and have served ever since as 
the basis of astronomical calculations. But the importance 
of the work does not consist in the mere statement of these 
laws ; it consists in the mathematical process by which they 
are applied to the resolution of the movements of celestial 
objects into rectilinear movements (5 > 

724. In the following century many illustrious mathema- 
ticians and astronomers carried on the work begun by 
Newton, which may be said, in a certain sense, to have been 
completed early in the present century by Laplace, in France, 
and by Gauss, in Germany. These writers brought into 
systematic form the results of investigations made by them- 
selves and their predecessors, which enable the astronomers 
of the present day to account completely for those move- 
ments of the celestial bodies which were known in the time 
of Newton. But modern astronomical improvements have 
brought into notice so many new facts, that the process of 
explaining observed movements by the mathematical devel- 
opment of the laws of motion is as far as ever from coming 
to an end. It may be noticed as a curious fact that the 
movement called the secular acceleration of the Moon, which 
Laplace supposed himself to have wholly accounted for, is 
now considered to be only partly clue to the causes proposed 
by him. Recent inquirers attribute the rest of this secular 



Sec. 724.] History of Astronomy. 365 

acceleration to a gradual slackening of the Earth's rotation, 
ch is itself accounted for by the action of the tides. lUit 
the period of the Earth's rotation is thus so slowly length- 
ened, that, according to one estimate, it is now only about 
a second longer than it was eighty thousand years ago. 

725. Newton distinguished himself in optics almost as 
much as in mechanics. His experiments on light showed 
for the first time that different kinds of light differ in reiran- 
gibility. He discovered the principle of the sextant, though 
he never published this discovery ; and he was the first to 
m.ike a reflecting telescope, although the principle of the 
instrument had been previously known. Reflecting tele- 
scopes were improved in the next century, towards the close 
of which Sir William Herschel made rerlectors more power- 
ful than any other telescopes of his time. With these, he 
made numerous additions to our knowledge of the planets, 
one of which, Uranus, was first noticed by him, although it 
had been seen by others, who took it to be a star. Sir 

lliam Herschel, too, was the first to show that some of 
the double stars are binary stars. Achromatic lenses 
were brought into notice by Dollond near the middle of the 
eighteenth century, and since manufacturers have become 
able to make large disks of glass, from which powerful achro- 
matic combinations of lenses may be formed, refracting tel- 
escopes have been generally preferred to rerlectors. It is not 

£, however, since Lord Rosse built great reflectors, the 
speculum of one of them being six feet across ; and still 
more recently, a large reflector has been mounted at the 
Observatory at Melbourne, Australia. 

726. The velocity of light and the distance of the Sun are 
subjects so connected with each other that the discoveries 
made respecting them may be jointly considered. If we 
know the Sun's distance, we know the length of the Earth's 

it, and can calculate what differences of aberration (551) 
will result from the rate of our movement round the Sun 
compared with the rate at which light moves. This last r.ite 
may then be determined I the annual aberration 



366 Outlines of Astronomy. [Sec. 726. 

of the stars (555). Again, if we know the Sun's distance, 
we can determine the velocity of light by the times of the 
eclipses of Jupiter's satellites ; for when Jupiter is in oppo- 
sition, its distance from the Earth is less than it is when 
Jupiter is in conjunction, by about twice the Earth's m 
distance from the Sun. Now by repeatedly observing Jupiter 
for a few days at a time, the rate at which its satellites move 
round it may be noticed, and Tables (707) of their motion 
may be formed. Hence the times of their eclipses may be 
predicted without regard to the velocity of light. It" these 
predictions are made right for the time when Jupiter is in 
opposition, the eclipses of Jupiter's satellites will be observed 
at other times later than they should be according to predic- 
tion ; and the time required for light to cross the Earth's 
orbit may thus be ascertained. If, then, the width of this 
orbit is known, we may find the velocity of light 

727. On the other hand, if we know the velocity of light, 
we may reverse either of these pi and thus find the 
Sun's distance. 

728. The usual way of finding the Sun's distance without 
knowing the velocity of light is, as we have seen, to find the 
distance of Venus or Mars, by means of the parallax of either 
of these planets ; then, by Kepler's third law, the times of 
the sidereal revolutions of the planets will determine their 
respective distances from the Sun. 

729. Although Tycho Brahe^s observations of Mars were 
much better than those of earlier astronomers, Kepler could 
not accurately determine from them the planet's para! 
With the instruments contrived by Picard (71 8), observa- 
tions could be made far more accurately than in Tycho's 
time ; and observations of the parallax of Mars were made 
with tolerable success in 1672 by Picard, Roemer. and C 
sini in France, and by Richer at the island of Cayenne, about 
5 north of the equator. On Richer's return to France, his 
observations, with those of the observers at French stati 
were discussed by Cassini, who concluded the parallax to be 
such as to make the distance of the Sun nearly what we now 



Sec. 729.] History of Astronomy. 367 

consider it to be. Tin's good result was mainly accidental, 
for the observations made were not accurate enough to war- 
rant any precise conclusion ; but since they were numerous, 
their mistakes were likely to balance each other sufficiently 
to give a tolerably correct parallax. Richer made various 
other observations at Cayenne besides those of the place ot 
Mars ; and he noticed that the pendulum of a clock which 
: correctly in France had to be slightly shortened to keep 
the clock from running slow at Cayenne. This was the first 
direet experiment which tended to show that the general laws 
of motion require us to regard the Earth as having a move- 
ment of rotation (160). The still more direct proofs of this 
conclusion by means of experiments with the free pendulum 
jo), and with the gyroscope (133), were contrived in 1S51 
and 1S52 by Foucault. 

730. A few years after Richer's voyage, Roemer noticed 
that the observed times of the eclipses of Jupiter's satellites 
could be best explained on the supposition that light required 
time to come from an object to the observers eye ; but he 
seems not to have followed out this line of research very 
thoroughly. 

731. The transits of Venus in 1631 and 1639 had passed 
out being used for observations of parallax, which would 

;ed have scarcely been practicable at that period. Kepler 
predicted the transit of 1631 ; his Tables were not sufficiently 
correct to predict the transit of 1639, which was observed, 
however, in England by Horrocks and Crabtree. Kepler was 
aware that there would again be a transit of Venus in 1761, 
and H illey, in one of his astronomical works, called the 
attention of astronomers to this transit, and pointed out a 
method of obtaining from it a correct determination of parallax 
bv means of the observed duration of the transit as seen from 
different terrestrial stations. It is obvious, for instance, that 
if an observer in the northern hemisphere sees the planet | 
over the centre of the Sun's disk, an observer in the south- 
ern hemi>phere will see the ; 5S north of the cen- 
tre of the disk ; and tl that the visual angle between 



368 Outlines of Astronomy. [Sec. 731. 

the lines from the extremities of its path across the d 
will be less than the corresponding angle through which the 
first observer sees it pass. It does not follow that the duration 
of the transit seen by the first observer will be greater than 
that seen by the second ; for this duration partly depends on 
the speed with which the observer is carried along by the 
Earth's rotation, which usually tends to shorten the transit, 
since the planet's movement at its inferior conjunction is ret- 
rograde, while that of the Earth's rotation is direct. We 
must therefore take the exact latitudes of the ol into 

account ; by doing this, we may calculate, from their observa- 
tions of the duration of the transit, how much farther from 
the centre of the Sun's disk the planet seemed to one 
server than it seemed to the other, in the middle of its transit. 
This will show the relative parallax of Venus and the Sun. 

732. The transits of Venus occur in June or in December; 
this depends, of course, on the pi. ice of the nudes of the 
planet's orbit, since the planet must be nearly in the plane 
of the ecliptic in order that it may come between the Earth 
and the Sun. Since its transits happen when the Sun is 
constantly in sight from either the arctic or the antarctic 
regions of the Earth, an observer may be stationed SO 

to look at a transit of Venus about the time of the lower 
culmination of the Sun ; and in this case, the transit will be 
prolonged, instead of being shortened, by the effect of the 
Earth's rotation. 

733. Since the Earth's rotation during a transit of Venus 
always changes the place of an observer, not stationed at one 
of the poles, with respect to the line joining the centres of 
Venus and the Earth, observations of the transit made in 
only one terrestrial place maybe used in calculating parallax. 
So, too, when the apparent place of Mars is compared with 
those of stars nearly in a line with it. its parallax may be 
determined by observations in one place at different times 
of night. But in order to obtain the best possible results, 
observations made in different places must be compared 
together. Halley, as has been said, proposed a system of 



Sec. 733.] History of Astronomy. 369 

(dating parallax from the differences of the durations of a 
transit at different places ; those places at which, as compared 
h others, the transit occupies a decidedly long or a deci- 
dedly short time being the most advantageous stations for 
observing it. Another method, proposed by Delisle, does not 
absolutely require the observation at each place of both the 

nning and the end of the transit. It depends on the com- 
parison of the times at which the transit begins or ends in 
different places. But this method supposes the longitudes of 
these places to be very well known. 



Note.— For the last sentence of section 731, substitute the following 
sentence : This will enable us. since we already know the relative distance 
of Venus and the Sun. to calculate the parallax and the distance of either. 



and combined with others made in Europe. The parallax 
of the Sun may be directly obtained from its zenith distances 
when it culminates at different terrestrial stations ; the zenith 
distances of stars being also observed at these stations. 
There will be no difference due to parallax between the ap- 
parent places of the stars observed at different places, while 
there will be some difference of this kind in the case of the 
Sun ; but this method is not very exact. However, La Caille's 
determination of the Sun's distance, by all his various methods, 

- more trustworthy than any previously obtained, although 
it differed more than the determination of Cassini from that 
now considered correct. 

735. In observing the transits of 1761 and 1769 nothing was 
attempted of importance, except to note the precise moments 
at which the planet seemed to the observer to have completely 
entered upon the Sun's disk, and at which it began to quit 
the disk at the close of the transit The 1 ititudes and longi- 
s of the places of observation were of course determined 
24 



368 Outlines of Astronomy. [Sec. 731. 

the lines from the extremities of its path across the disk 
will be less than the corresponding angle through which the 
first observer sees it pass. It does not follow that the duration 
of the transit seen by the first observer will be greater than 
that seen by the second ; for this duration partly depends on 
the speed with which the observer is carried along by the 
Earth's rotation, which usually tends to shorten the transit, 
since the planet's movement at its inferior conjunction is ret- 
rograde, while that of the Earth's rotation is direct. We 
must therefore take the exact latitudes of the observers into 

♦' <">r mIkitv.i- 



ot tire cmyuv ... -. 

and the Sun. Since its transits happen when the Sun is 
constantly in sight from either the arctic or the antarctic 
regions of the Earth, an observer may be stationed so 
to look at a transit of Venus about the time of the lower 
culmination of the Sun ; and in this case, the transit will be 
prolonged, instead of being shortened, by the effect of the 
Earth's rotation. 

733. Since the Earth's rotation during a transit of Venus 
always changes the place of an observer, not stationed at one 
of the poles, with respect to the line joining the centres of 
Venus and the Earth, observations of the transit made in 
only one terrestrial place maybe used in calculating parallax 
So, too, when the apparent place of Mars is compared with 
those of stars nearly in a line with it, its parallax may be 
determined by observations in one place at different times 
of night. But in order to obtain the best possible results, 
observations made in different places must be compared 
together. Halley, as has been said, proposed a system of 



Sec. 733.] History of Astronomy. 369 

calculating parallax from the differences of the durations of a 
transit at different places ; those places at which, as compared 
with others, the transit occupies a decidedly long or a deci- 
dedly short time being the most advantageous stations for 
observing it. Another method, proposed by Delisle, does not 
absolutely require the observation at each place of both the 
beginning and the end of the transit. It depends on the com- 
parison of the times at which the transit begins or ends in 
different places. But this method supposes the longitudes of 
these places to be very well known. 

734. Before the time for the transits of 1761 and 1769. the 
movements of all the planets had been much better deter- 
mined than they had been in the previous century, so that the 
time at which the transits would be seen could be well calcu- 
lated, although not as well as the time of the transits of 1874 
and 1882 could be calculated a hundred years later. Mean- 
while, the parallax of Mars, of Venus near its inferior conjunc- 
tion, and of the Sun, had been computed by La Caille from 
observations of his own, made at the Cape of Good Hope, 
and combined with others made in Europe. The parallax 
of the Sun may be directly obtained from its zenith distances 
when it culminates at different terrestrial stations ; the zenith 
distances of stars being also observed at these stations. 
There will be no difference due to parallax between the ap- 
parent places of the stars observed at different places, while 
there will be some difference of this kind in the case of the 
Sun ; but this method is not very exact. However, La Caille's 
determination of the Sun's distance, by all his various methods, 

s more trustworthy than any previously obtained, although 
it differed more than the determination of Cassini from that 
now considered correct. 

735. In observing the transits of 1761 and 1769 nothing was 
attempted of imjx>rtance, except to note the precise moments 
at which the planet seemed to the observer to have completely 
entered upon the Sun's disk, and at which it began to quit 
the disk at the close of the transit The latitudes and longi- 
tudes of the places of observation were of course determined 

24 



370 Outlines of Astronomy. [Sec. 735. 

as well as might be. But it was found unexpectedly difficult 
to tell when the planet ought to be regarded as just within the 
border of the disk. Instead of appearing at this time as a 
round black spot, it seemed pear-shaped, as if it were attached 
to the limb of the Sun, after crossing it, by an elastic fasten- 
ing. When this " black drop " broke and disappeared, the 
planet looked circular, but seemed to be already somewhat 
within the Sun's limb. As it approached the part of the limb 
where it was to quit the disk, a like distortion took place, so 
that the observers found it as difficult to determine the exact 
time of the end of the transit as to determine exactly when it 
began. Irradiation is regarded as the cause of the perplexing 
appearance just described. 

736. From this and other causes, no result of importance 
was obtained from the observations of the transit of 1761. 
The result of the observations of 17' much better, 

although the moments of the beginning and end of the tran- 
sit witnessed by each ol (server were again rendered to some 
extent uncertain by the effects of irradiation. The dis 
which arose as to the right result to be obtained from th< 
observations has lasted to our own time. Still, the transit 
of 1769 showed conclusively that the mean distance of the 
Earth from the Sun is from ninety to one hundred millions 
of miles. 

72>7- Among the most important of the expeditions under- 
taken for the observation of the transit of 1769. were the 
English expedition to Tahiti (under the command of the 
celebrated explorer, Captain Cook), the Danish expedition 
to Lapland, and a French expedition to California. An ob- 
servation at Pondicherry, in India, which was to have been 
made by the French astronomer Le Gentil, was prevented by 
clouds ; and this failure must have been unusually annoying 
to the observer, as he had stayed eight years in the E 
Indies for the purpose of observing the transit. He had 
originally intended to observe the transit of 1761 at Pondi- 
cherry, but, owing to a war which was then going on between 
the French and English, in the East Indies, he had been 



Sec. 737.] History of Astronomy. 371 

obliged, on that occasion, to remain at sea, where lie saw the 
sit without being able to observe it to any good purpose. 
75S. In the present century, a great variety of means have 
been tried to determine the Sun's distance ; among the chief 
of these are observations on Mars. The best observations 
for the parallax of Mars are those taken at stations differing 
considerably in latitude, but little in longitude, so that the 
planet may be observed at about the same time, and under 
like circumstances, at each station. But observations made 
at a single station early and late in the night are also service- 
able (733)- 

. It was not until recently that any determination could 
be made of the velocity of light, independent of the Sun's 
distance (727). The English astronomer Bradley discov- 
1 the facts of aberration (and also of nutation) by obser- 
ions of the zenith distances of stars, made during the last 
century. Bradley was also the first to make observations of 
the stars accurate enough to serve as a means of determining 
proper motion. But although the observed aberration of the 
stars, and the observed eclipses of Jupiter's satellites, show 
the time required (about eight minutes) for the passage of 
: over a distance equal to that between the Earth and the 
Sun, we still require the knowledge of this distance to deter- 
mine the velocity of light. In the present century, however, 
means have been found for the direct measurement of the 
rate at which light moves. Experiments on the velocity of 
light have lately been made by Cornu ; their results were an- 
nounced in 1873. They were made at Paris with an appara- 
tus similar to one which had been contrived and used in 1 
by Fizeau, several refinements, however, being introduced 
into the work. 

eral principle of these experiments is as fol- 

- : let the light of a lamp near the observer be 1 

back to him from a distant mirror. Place a wheel near the 

rand the lamp, so that the ligl mirror 

veen the s of this wheel, and returns to the eye 

after again passing between these spokes. We will 



372 Outlines of Astronomy. [Sec. 740. 

that the distance from the wheel to the mirror is half a mile ; 
the light, accordingly, travels one mile between its first and 
second passages through the wheel. Let the spokes of the 
wheel taper towards the centre, and be everywhere just as 
wide as the spaces between them at the same distance from 
the centre of the wheel. Now if the wheel is turned at such 
a rate that the spokes, at the instant of the return of any par- 
ticular part of the light, have just taken the places occupied 
by the openings through which that light went out to the mir- 
ror, it will be kept from reaching the eye, provided it comes 
back exactly in the opposite direction from that in which it 
went out. Hence, if each spoke moves through its own 
width in the time taken by light to go one mile, the observer 
will see no reflection at all ; the wheel will act as an opaque 
screen. If the rate of its revolution is known, when this 
effect is produced, the speed at which light travels through 
the air may be calculated. 

741. In practice, the light which is to be reflected must be 
reduced by suitable lenses to a small beam composed of 
pencils each of which is a nearly parallel pencil (435). The 
general direction of this beam is that of a line perpendicular 
to the distant mirror from the observer's eye. so that it 
comes back in exactly the opposite direction. It may seem 
as if this could not be done without setting the lamp exactly 
in front of the observer or behind him; but the lamp may 
stand at one side, and part of its light may be turned into 
the right direction by a slanting piece of glass through which 
the observer sees the returning light. The light goes out 
between the teeth on the edge of a wheel, which may be 
made to turn by mechanical contrivances as much as eight 
hundred times in a single second, if necessary : these teeth 
answer, since the beam of light is small, instead of the 
spokes we supposed the wheel to have. Assuming that the 
number of teeth is two hundred and fifty, it will take only 
T Jo of one revolution of the wheel to move the teeth into the 
places of the openings between them. If the wheel turns 
four hundred times in a second, -gJo °^ one revolution will 



Sec. 741.] History of Astronomy. 373 

take only — — part of a second : and as light moves less 
than two hundred thousand miles a second, four hundred 
revolutions of the wheel in a second are even too many for 
the object of making the light disappear, if, as we have sup- 
>ed, the wheel is half a mile from the distant mirror. In 
fact, if the wheel is at first turned slowly, and if its speed is 
lually increased, the reflected light seen by the observer 
becomes dimmer, disappears when the wheel has attained a 
certain speed, and afterwards comes into view again, reach- 
its full brightness when the wheel turns twice as fast as 
at the time of the disappearance of the light. By continuing 
to increase the speed of the wheel, the light may be made to 
disappear again. The rate at which the wheel turns, and 
the signals by which the observer marks the disappearances 
and reappearances of the light, may be registered by elec- 
tric apparatus. As the theory of refraction requires us to 
suppose slight differences in the speed of light through 
media of different refracting powers, the speed of light qut- 
side of the atmosphere must be calculated by known rules 
from its speed within the atmosphere determined by the 
experiments just described. 

742. In Cornus recent experiments, the wheel was about 
10,310 metres, or nearly six and a half miles, from the dis- 
tant mirror, which of course made the experiments easier 
and more trustworthy than they would have been if the 
distance had been small. Their result is that light moves 
beyond the atmosphere at the rate of 298,500 kilometres, or 
about 185.500 miles, in one second. The distance of the 
Sun, calculated from this velocity (727), agrees with the 
results of recent observations of parallax. 

743. It is expected that the results of the observations of 
the transits of Venus in 1874 and 1S82 will considerably in- 
crease the accuracy of our knowledge of the Sun's dista;. 

It will be shown in the following chapter that our knowl- 
.c of this distance, on which our knowledge of all greater 
distances depends, is as yet far from a 
ditions have been fitted out by the chief civilized nations 



374 Outlines of Astronomy. [Sec. 743. 

for the observation of the transit of 1874 at all available J 
places which arc is for such observations. I 

The observers who are to note the times at which tin 
begins and ends have been exercised in tl 
artificial imitations of the transit, .so that they may I 
iar with the deceptiv >n. But we ! 

now other kinds rvations to rely ii}'<»n. Numer 

photographs of the Sun will be taken during the trai 
and the place of the planet on the disk at particular times ' 
and stations will be determined by the measurement of these 
photographs. M <>f the plane 1 he 

made during the transit with instruments known as In 
meters. A heliomet 1 

in two. the puts being made to slide upon each other so that 
two images of any ol 

can be brought I tit coin< i f the im- 

jome oth 
two parts of the ol 3 with r< :h< r 

which is needed to bring about this coinciden s to 

measure the visual angle between I 

744. The expeditions sent out by the Unit 

cupy stations in China. Asiatic 1 ind Japan, in 

northern hemisphere, and various islands in the southern 
hemisphere. English, French, German, and R Kpe- 

ditions occupy similar situations in varii the 

Earth. The transit occurs December 8, after midnight in 
Greenwich astronomical mean time, and hence DccermV 
in civil time. 

745. The transit of 1SS2 will be visible along t 1 

coast of the United States. It happens on the afternoon of 
December 6 in Greenwich time. 

740. Closely connected with the subjects of the distance of 
the Sun and of the speed of light is that of the distances 
the stars. No star was proved to have a noticeable parallax 
before the present century : but Bradle] iber- 

ration, and Herschel's of the existence of bin.;: had 

their origin in attempts to determine parallax. In 1N38, the 






Sec. 746.] History of Astronomy. 375 

parallax of a star in the constellation Cygnus (fir Cy^ni x was 
determined by Bessel, who had been comparing the apparent 
place of that star with those of others near it by means of 
a heliometer. Soon afterwards appeared Henderson's an- 
nouncement that the chief star of the Centaur (u Centauri) 
showed a parallax amounting to nearly 1". That is, the ap- 
parent places of this star, as seen at any time from the Sun 

and from the Earth, would differ by about 1", or the -~ 

part of the horizon or any other great circle of the celes- 
tial sphere. This is the greatest parallax yet discovered 
in any star ; but, great as it is. it shows, as has been said 
(559), that the star is over two hundred thousand times as 
far from us as the Sun is ; so that, as light takes about eight 
minutes to come to us from the Sun, it must take over one 
million six hundred thousand minutes, or more than three 
years, to come from a Centauri. Since 1S38, many stars 
have been proved to have some parallax. 

747. Various parts of the Earth have been surveyed, both 
in the last century and in this, with a precision much beyond 
it was possible in Picard's time. In this way the shape 
of the Earth has been shown to be very nearly in accordance 
with that assigned to it by an estimate of Newton's. One of 
the best computations of the figure of the Earth is that made 
by the distinguished German astronomer Bessel (the dis- 
coverer of the parallax of 61 Cygni) from his own obser- 
vations and those of others. Bessel also did much to advance 
our knowledge of the proper motions of stars by accurately 
determining their apparent places. But this investigation has 
little interest except to professional astronomers, si nee the 
results to be obtained from it are yet distant. The apparent 
places of stars, however, are of constant use in all op< ratit QS 
undertaken by astronomers and surveyors. 

. Perhaps the most remarkable astronomical (list 
of this century was that of the planet Neptune, the appal 
place of which was correctly predicted by Le Verrier in Kra 
and by Adams in England, merely by means of the p< rturba- 
tion^ it had been producing in the movements of Uranus. It 



376 Outlines of Astronomy. [Sec. 748. 

was discovered, by means of the prediction of Le Verrier, in 
1846. The discovery of asteroids began about the beginning 
of this century, and of late has gone on with great rapid it 

749. The researches in optics, to which we owe all the dis- 
coveries made with the spectroscope, began with the o, 
vation of dark lines in the solar spectrum by Wollaston, in 
1802. The discovery was due to the use of a slit to admit the 
light, instead of a round opening, such as Newton used in 
his experiments on the refraction of light. Hut the ex] 
ments of KirchhotT and Bunsen, about i860, were th< 
which resulted the great interest and the rapid progress of 
spectroscopic work at the present day. 

750. One of the first uses made of astronomical ol^ 
tions was their application to the measurement of time. The 
ancient Greeks and Romans were in the habit of dividing the 
time from sunrise to sunset into twelve hours, and the night 
likewise into twelve hours. These hours, accordingly, had 
no fixed length, but varied according to the season of the 
year. This was of no great importance for ordinary purpoa 
but the impossibility of making an exact year out of any whole 
number of days gave the ancients much trouble. The Egyp- 
tians decided on calling three hundred and sixty-five days a 
year, and dividing these days into twelve months of thirty 
days each, with five days between 4 fhe end of the twelfth 
month and the beginning of the first month of the next year. 
This was a systematic method, very convenient in keeping 
account of time, but according to which each legal, or civil, 
year began a little earlier in the tropical year than the preced- 
ing civil year had begun. Accordingly, the Egyptian civil 
year began in all seasons, one after another, until finally the 
civil year began at about the same time in the tropical year as it 
did 1,460 tropical years or 1,461 civil years before. This length 
of time is sometimes called the Sothiac period. A period, in 
this sense of the word, or a cycle, which is a name of like 
meaning, is that length of time at the beginning and end of 
which different ways of measuring time agree. The agree- 
ment, of course, is seldom exact. 






Sec. 751.] History of Astronomy. 377 

751. The Greeks tried to count time by lunations, and also 
by tropical years. Their actual reckoning was consequently 
in accordance with neither. The Athenians are said to have 
decreed public honors to Meton, who pointed out that the 
time occupied by two hundred and thirty-five lunations differs 
little from that occupied by nineteen tropical years ; a dis- 
covery which seems to us of little consequence, because we 
no longer try to keep time by lunations. The period of 
nineteen years is called the lunar cycle, or the Metonic 
cycle. 

752. There is another lunar cycle which is nearly equal to 
that just mentioned. During two hundred and twenty-three 
lunations, the line of nodes of the Moon's orbit has retro- 
graded nearly nineteen times 360 with respect to the line join- 
ing the Earth and Sun. In other words, nineteen synodical 
revolutions of the Moon's nodes answer to two hundred and 
twenty-three synodical revolutionc of the Moon. No one, 
of course, ever counted time by the movements of the imagi- 
nary points called nodes ; but since eclipses of the Sun take 
place only when the Moon is near the plane of the ecliptic 
(or, in other words, near one of the nodes of its orbit) at the 
time of its conjunction, and eclipses of the Moon happen 
only when the Moon is in opposition, and near a node, the 
cycle just mentioned is a cycle of eclipses (370). That is, the 
eclipses which occur during any period comprising two hun- 
dred and twenty-three lunations follow each other at like 
intervals to those between the eclipses of the next two 
hundred and twenty-three lunations. As an eclipse of the 

1 Moon can be seen from any place at which the Moon is in 
sight at the time of the eclipse, it was noticed in very early 
times that each eclipse of the Moon was followed by another 
about eighteen years later, so that the eclipses of every 
eighteen years were repeated in the next eighteen years. 
Eclipses of the Moon could thus be predicted ; but this 
simple method of prediction was not well suited to ecli; 
of the Sun, because an eclipse of the Sun can only be seen 
from that part of the Earth within the penumbra of the Moon. 



37 8 Outlines of Astronomy. [Sec. 752. 

This cycle of two hundred and twenty-three lunations, or 
about eighteen years, is sometimes called the Saros. It is 
not an exact cycle, so that it affords no precise means of 
making predictions. 

753. Modern astronomers have noticed a number of cycles, 
like this cycle of eclipses, in the movements of various c< 
tial objects ; but all the effects which could be predicted 
means of these cycles can be predicted more accurate] 
the general rules on which tin s themsel end. 

Five revolutions of Jupiter around the Sun pretty rn 
correspond, for instance, to two of Saturn. Hence aris< 
peculiar disturbance of the movements of these planets. ki.< 
as the great inequality of Jupiter and Saturn, which requires 
about 918 years for the production of its effects. During 
this time the conjunctions of Jupiter and Saturn have hap- 
pened at a set of pla< es pretty evenly distributed round the 
orbits of the two planets. Another cycle is that of the ti 
sits of Venus. Might sit' is take up about one 

more than thirteen sidereal revolul 
sidereal years take up about 

real revolutions of Venus. The nodical and sidereal revolu- 
tions of Warns are nearly of the same length ^570). At any 
inferior conjunction of Venus, therefore, which happens eight 
years after one o( its transits, the planet has nearly reached 
the same place it had when the transit occurred with respect 
to the node near which the transit occurred. At the inferior 
conjunction which happens 235 years after the transit, it is 
a little beyond the place it had when the transit occurred with 
respect to the node near which the transit occurred. These 
cycles cannot both be exact, since 8 is not contained an 
exact number of times in 235 ; and in fact, as has just heeii 
said, neither is perfectly exact. If the cycle of eight years were 
exact, and a transit had ever happened at one of the nodes, 
there would be a transit every eight wars at that node, 
it is, there are ordinarily two transits at the same node two 
days less than eight years apart, and then no more at that 
till two days over 235 years from the last of the two transits. 



Sec. 753.] History of Astronomy. 379 

The transits of 1631 and 1630 took place near the ascend- 

node, or that at which Venus passes from south to north 

of the plane of the ecliptic. Adding 235 to 1639, we have 

74; there was no transit 235 years from 1631, as Venus 

- then too far past the ascending node at the time of its 
interior conjunction : but there will be a transit at that node 
in 1882. These transits take place in December (744, 745). 
The transits of 1761 and 1769 took place at the descending 
node, and so will those of 2004 and 2012, the first of which 
comes 235 years after 1769, not 1761, the transit of 1761 fail- 
ing to be repeated. The transits at the descending node 
happen in June. 

754. Examples of cycles like these might be made very 
numerous ; in fact, all periodical events happen in cycles of 
greater or less exactness. 

7SS- The Romans, like the Greeks, wished to make their 
civil years conform to the tropical year, and yet to reckon 
time with regard to lunations. Their calendar, of course, fell 
into confusion, the years being lengthened by the insertion 
of a number of days decided upon each year by the priests, 
with regard, it is said, rather to politics than to science. 
Julius Caesar put an end to this disorder by employing the 
astronomer Sosigenes to reform the calendar (302). As 
the exact length of the tropical year was still unknown, it 

- decided that the civil year should ordinarily consist of 
5 clays, and that an additional day should be inserted every 

fourth year. The period called a Julian year is accordingly 

365} days of mean time. The Julian period is a period of 

3o Julian years, assumed to be^in in the year 4713 B.C. ; it 

>f some use in the study of chronology, but not for any 

ary purpose. 

756. In the course of the sixteen centuries following the time 

'Jaesar. it became obvious that the time occupied by four 

rs was somewli.it less than the [,461 icfa 

make up four Julian years. Our present calendar • 

\ I I I , to 

p the vernal equinox as nearly as might be to the 21st of 



3B0 Outlines of Astronomy. [Sec. 756. 

March, on which it occurred at the time of the important 
ecclesiastical council held at Nice (or Nicaea) in Asia Minor, 
in the year a.d 325. This council had made rules for the 
time at which the church festival of Easter should be yearly 
celebrated ; and the rules thus made took it for granted that 
the vernal equinox happened on Marcli 21st. In the time 
of Gregory XIII., the day on which the vernal equinox hap- 
pened was March 11th, according to the Julian calendar. 
The reformation of the calendar was accomplished by omit- 
ting ten days, the clay after the 4th of October, 1582, being 
called the 15th of October; and to prevent the need of like 
changes in after times, it was determined that the years 1700, 
iSoo, and 1900, should have only 365 days, instead of 366, 
as they would have had under the old rule The year 2000, 
however, will have 306 days, according to the Gregorian cal- 
endar ; the years 2100, 2200, and 2300, 365 days each ; 2400 
will have 366, and so on. 

757. The Catholic nations of Europe immediately adopted 
the change made in the calendar by the Tope ; but other 
nations continued for a time, as the Russians do still, to use 
the Julian calendar. In England, the change from the Old 
Style to the New Style, as it was called, took place in 1752. 
As the year 1700 had 366 days, according to the Old Style, 
eleven days had to be omitted to make the calendar agree 
with that of Catholic nations. For legal purposes, the Eng- 
lish year, according to the Old Style, had been considered to 
begin on March 25th, the date of the church festival of the 
Annunciation. The introduction of the New Style, by stat- 
ute, set the beginning of the legal year at January 1. The 
legal year 175 1, in England, lasted only from March 25th to 
the end of December. 

758. The length and the name of each of our months have 
come down to us from the Romans, who made no permanent 
change in either after the time of Julius Caesar and his suc- 
cessor Augustus. The week was not used as a measure 
of time by the early Greeks and Romans, although it f 
in use in ancient times among various Eastern nations. 



Sec. 758.] History of Astronomy. 3S1 

The English names of the days of the week are mainly 
derived from the old Teutonic mythology. But these mat- 
ters form, properly speaking, no part of the history of astron- 
omy. 

759. We may say much the same of the numerous specu- 
lations made with respect to the distant past and remote 
future of the universe. Most of them can be made as well 
without any knowledge of astronomical subjects as with it, 
and, in tact, they are seldom made by professional astron- 
omers. 

760. It is usual, however, to consider what is called the 
nebular hypothesis as a part of the science of astronomy. 
This hypothesis was suggested by the German philosopher 
Kant, and also by the French mathematician Laplace, who 
has been named above as one of the most distinguished 
inquirers into the nature of planetary movements. The 
reason for regarding the nebular hypothesis as important is 
that it enables us to account on mathematical principles for 
certain facts observed in the Solar System, and directs our 
attention to the systematic observation of other facts; while 
most speculations on the early condition of the universe offer 
no opening for exact reasoning or the strict application of 
known laws, but are invented merely to account for what now 
exists by vague suggestions relating to matters which are at 
present wholly beyond the reach of observation and exact 
calculation. 

761. According to the nebular hypothesis, the matter now 
composing the various objects which make up the Solar S 
tern was once in the form of a nebulous mass, having 
movement of rotation. The temperature of this nebula 
high enough to keep it in the l radually 
cooled and shrunk together, while the I its rotation 
increased according to known laws. Its oul 

irated from the rest by tin- inertia I ired by this 

increasingly rapid rotation : and tl 
number of times. Each time 
ter was formed around the nebula : and the matter of eaeh 



382 Outlines of Astronomy. [Sec. 761. 

ring was ultimately either collected into a single planet, or 
into a group of bodies differing more or less in size. 

762. If any one wishes really to comprehend this hypoth- 
esis, he must take much more trouble and study much 
harder than most people either can or will. On the otl 
hand, no sound opinion can be formed about a theory which 
is hot thoroughly understood. It is not surprising, there- 
fore, that the opinions put forward about the nebular hy- 
pothesis are often worthless. The opinions of most men 
who know enough to discuss the hypothesis with profit seem 
at present to be in .favor of its truth. 

763. There are certain tacts which any one can see to be 
favorable to the nebular hypothesis. The existence of la 
gaseous bodies seems to have been proved by the spectro- 
scope ; it was formerly doubted. Modern geologists seem 
decidedly to think that the Earth sends out more heat than 
it receives from the Sun, stars, nr or any other 
sources. The ring of Saturn, whether it is or is not made 
up of small satellites, presents us with i tual 
formation by some means of an object most easily accounted 
for by the repetition on a smaller scale of the process by 
which Saturn itself was formed. 

764. But it is still too early for most of us to regard the 
nebular hypothesis as more than a useful supposition, which 
tends to direct our observation to the actual condition of 
the Earth, as well as to that of the Sun and of the nebulae, 
so far as their condition can be observed. 

765. The ordinary supposition with regard to the future 
of the Solar System is that the various bodies of which it 
consists will continue to cool for an indefinitely long time, 
while the resistance of the ether or of other matter through 
which they may be moving will gradually bring all the plan- 
ets to the Sun. Hence the Solar System would finally come 
to consist of the Sun alone, deprived of its light and heat. 
and destined in the lapse of ages to become part of some 
larger body by a continuation of the process which had put 
an end to the separate planets. 



Sec. 766.] History of Astronomy. 3S3 

766. Another speculation regards the fall of the planets 

the Sun as sufficient to produce heat enough to restore 

these bodies to their former nebulous condition. But accord? 

ing to modern views regarding what is called the dissipation 

of energy, the final result of all changes would be to extinguish 

motion, and uniformly diffuse heat, throughout the universe. 

- j. It is to be observed, however, that under the actual 

limitations of human knowledge we are brought in the con- 

E ration of all questions like those just mentioned to the 
subject of infinity. We cannot regard time otherwise than 
as infinite, because we have no experience of any cessation 
of time. On the other hand, we can regard all events as 
coming to a stand, because particular events are observed to 
do so. Water thrown on the roof of a house runs off upon 
the ground; but if it falls into a hollow metal basin, it 
settles into the lowest part of the basin and comes to rest. 
So, too, a hot iron gradually comes to the temperature of the 
air around it, and ceases to cool. 

768. But if we regard time as a quantity, we see that it is 
constantly lost and never replaced. If we did not take it for 
granted that there is an infinite amount of time to draw upon, 

should suppose that time must some day be all used up. 
The course of events, then, when regarded as time, seems 

.ess or not as we please. So, too. when we regard it on 
mechanical principles, we find it tending to a close, unless 
we please to regard it as endless ; or, in other words, unless 
we regard the stock of available energy in the universe as 
infinite. We soon come, both in the case of time and in that 
of energy, to the limit of human knowledge, which we call 
infinity. 

We cannot, then, accept any speculations with n 
to the distant future as forming part of scien< 
encountering the impossibility of learning any thing which is 
infinite, we are obliged in these s; nd the 

application of what we call the laws of nature to ol 
rem md time that we have little security in pre- 

dicting any thing with respect to tfa 



384 Outlines of Astronomy. [Sec. 770. 

770. That every thing we can observe is in a state of 
change is perhaps the most general law which we can form 
at present ; and we may reasonably think, whatever gue- 
we make about the past and future of the Solar System, that 
the Earth was not always, and is not always to be, a suitable 
dwelling-place for mankind, or for any creatures nearly re- 
sembling mankind. But even this is an idle speculation. 
God's ways are not our ways, nor are his thoughts our 
thoughts. The laws of nature, to which our thoughts are 
confined, are necessarily mere fragments of the great 01 
of nature which exists, as we hope, by the authority of an 
infinite Creator, to whose wisdom and goodness we may 
trust. All our sciences consist in the study of such parts 
of God's works as are within the reach of our faculties 1 
not in conjectures carried so far beyond the bounds of our 
knowledge that they fail to point out to us what we should 
next observe. 



Sec. 771.] Notes, References, and Statistics. 385 



CHAPTER XVI. 

NOTES, REFERENXES, AND STATISTICS. 

— 1. The following abbreviations of the titles of works 

will be employed in this chapter. In the references to be 

n, Arabic numerals will denote the page referred to 

(with the exceptions named below), and Roman numerals the 

volume. 

A. American Ephemeris and Nautical Almanac for 1S77. 

C. Comptes Rendus Hebdomadal res de l'Acadcmie dcs 
Sciences (Paris). 

D. Astronomical Observations and Researches made at 
Dunsink, the Observatory of Trinity College, Dublin. 
Second Part. Dublin, 1S73. 

G. Hypsometrical Tables, in the ''Tables, Meteorological 
and Physical, prepared for the Smithsonian Institu- 
tion bv Arnold Guyot. Second edition. Washington, 
1858." 

H. Papers by W. Her^chel. read before the Royal Society 
of London (referred to by the years in which they were 
read). 

J. American Journal of Science and Arts (referred to by 
the year, volume, and page). 

L. Annalen der Sternwarte in Leiden, Band III. Haag, 
1S72. 

II Memoir^ of the Royal Astronomical Society, London. 
Monthly Notices of ditto. 

N. Astro nomische Xachrichten (referred to, as usual, only 
by the number of that periodical containing the article 
cited). 

O. Outlines of Astronomy, hy Sir John F. W. Ilerschel. 
Fifth edition. London, 1S58. 



386 Outlines of Astronomy. [Sec. 771. 

P. Annales de l'Observatoire Imperial de Paris. Mem- 
oires. 

S. Die Sonne, von P A. Secchi Autorisirte Deutsche 
Ausgabe und Originalwerk, herausgegeben durch Dr. II. 
S^hellen. Braunschweig, 1S72. 

\V. Appendix II. to the " Astronomical and Meteorological 
Observations made at the United States Naval Obsc 
torv during the year 1S65." 

Z. Ueber die Nfatur tier Cometen. Yon Johann Carl Fried- 
rich Zollner. Leipzig, 1S72. 

772. Dimensions of the Earth. On the assumption that 
the Earth is a geometrical oblate spheroid of revolution, its 
equatorial and polar semidiameters were determined 1 
as follows (X. 438): — 

Equatorial •eraidiameter . . . 3.-7-. 077. 14 toi 
Polar „ ... 3,361,139.33 

Ratio of the difference between the>e numbers to the first 
to the second 



999.1538 ' 

These results were derived from computations founded on 
the measurements, at different times and in different part- 
the Earth, of ten arcs of meridians. The value of 1 t 
in English fathoms was taken by Bessel (N. 333) to be 
1.06576542 ; hence 1 toise contains 6.3 English ' 

Others reckon (G. 115) 1 toise to be equivalent to 6.394590 
English feet or 6.394219 American feet With these last 
values, we find from Bessel's results : 

Equatorial diameter cf the Earth 41.S17.1S4 English 

„ ,, ,, „ ,, 41.S44.756 American ,, 

„ „ „ „ ,, 7.925.14 .. miles. 

Polar ,, „ ,, ,, 41.707.29S English feet 

„ „ „ „ ,, 41.704.S7S American „ 

11 n n m n 7-SoS.65 „ miles. 

The following results were obtained by Clarke from data 
partly the same as Bessel's ; see p. 773 of the Account of 
the Principal Triangulation in the Ordnance Survey of Great 
Britain and Ireland. London, 1S58. 



Sec. 772.] Notes, References, axd Statistics. 3S7 

Regarding the section along the Earth's axis as not neces- 
sarily elliptical in shape : 

Equatorial semidiameter 20.927.197 English foot. 

Polar ,. 20,855,493 

Half ratio of sum to difference of these numbers 291.36. 

Regarding the section as elliptical : 

Equatorial semidiameter 20.926. 34S English feet. 

Polar „ 20.S55.233 

Half ratio of sum to difference of these numbers 293.76. 

Another determination by Clarke is as follows (M. xxix. 
39) : the assumption in this case being that the Earth is an 
ellipsoid, but not an ellipsoid of revolution, so that its equator 
is an ellipse. There is some ground lor tins assumption, but 
further surveys are required to determine the shape of the 
equator with certainty (M. xxix. 42). 

Longest equatorial semidiameter,^ 

in longitude 13 5S/5 east from ^20.926,485 English feet. 

Greenwich J 

Shortest equatorial semidiameter, -\ 

in longitude 103 5S'-5 east from 120.921,177 ,, ,, 

Green wich J 

Polar semidiameter 20.S53.768 ,, ,, 

Fergola. in a treatise on the relative positions of the Earth's 
axes of rotation and of figure, published at Naples in 1874, finds 
from the surveys hitherto made that, supposing the Earth to 
have the form of an oblate ellipsoid of revolution, its axis of 
rotation is inclined i° 8'. 4 to its shortest axis, and that, if we 
reckon longitude by meridian planes passing through the 
shortest axis, the north pole of rotation is 239 31 '.5 east of 
Greenwich. 

Latitudes and Longitudes of Observatories. In the 

following table, the sign -|- before a latitude signifies north 

and — south : before a longitude -f" si| the 

:ed States Naval Observatory at Washington, and — east 

of it (A. 475. 476). 



3 88 



Outlines of Astronomy. [Sec. 773. 



Place. 


Latitude. 


Longitude. 


Berlin, Prussia 

Cambridge, Massachusetts .... 
Cape of Good Hope, Africa . . . 

Chicago, Illinois 

Greenwich, England 

Madras, India 

New York, N. Y 

Paramatta (near Sydney)) New South 

Wales ' 

Paris, Fiance 

Santiago, Chili 

Washington, I). C 


/ // 

+ 52 30 

+ 42 22 48.1 

— 33 S ( > 3 2 
+ 41 50 1.0 
+ 51 28 

+ 13 4 
+ 40 43 1 

— 33 

n 

— 3 1 


H. m. s. 

— 6 1 47.50 

— 23 4?. 11 

— 6 22 7.82 
+ 42 

— 5 8 12 12 

— 10 29 9 40 

— 12 15.47 

— I 5 12 

~ 5 »7 ; 

— 25 
00 



Latitude of Telegraph Hill, San Francisco, California, -f-37 
48' 6". I by note on a chart in United States Coast Survey 
Report for 1852. Longitude of a Coast Survey station at San 
Francisco, in 1869, 3 h 25™ 7'. 33 west of Cambridge Observatory 

(j. 1872, hi. 398). 

These data may aid in the approximate determination of 
Other latitudes and longitudes by means of maps. 

774. Refraction and Dip, according to the tables in Chau- 
venet's Spherical and Practical Astronomy. Mean refraction, 
at io° zenith distance, o' io".3 ; at 45 zenith distance, 
o' 58". 2 ; at 8o° zenith distance, 5' 19". 2 ; at 90 zenith dis- 
tance, 36' 29". These examples illustrate the rapidity with 
which refraction increases, near the horizon, with the increase 
of zenith distance. 

Dip of the sea horizon, when the eye is 5 feet above the sea 
level, 2' 1 1" ; at a height of 10 feet, 3' 6" ; at a height of 100 
feet, 9' 48". 

775. Rotation of the Sun. In studying the rotation of 
the Sun, the values of the following quantities are investi- 
gated : — 

The period of rotation, expressed in days of mean time, 
which we may denote by T; or the angle through which the 
Sun turns in one day of mean time, denoted by f. 

The heliocentric longitude of the ascending node of the 
Sun's equator, denoted by 3. 



Sec. 775.] Notes, References, and Statistics. 3S9 

The angle between the planes ol the ecliptic and of the 
Sun's equator, denoted by /. 

Recent attempts to determine these quantities have led to 
the following results. The dates (called epochs) to which 
the determinations are meant to apply are always given in 
work of this kind, since no determination can he true except 
for some particular time, owing to the continual shifting of 
the vernal equinox and other points with reference to which 
our* computations are made. But in the case now before us, 
the disagreements between results obtained within a lew 
years of each other are much greater than the amounts, dur- 
ing the intervals between the epochs of these results, of the 
changes due to the cause just named. 

Laugier found (C. xv. 941) for the beginning of 1843, 
T= 25.34 « =75°S' i = 7°9'- 

Spore r (N. 1615) found from his early observations, T = 
25.1S33 Q =74° 11' 6' f = 6° 54' 43"; and from a later set, 
T = 25.2590 Q =74° 47' 46'' 1 =6° 58^5"; combining these re- 
sults with regard to the number of observations on which 
each depends, he concluded, for the middle of 1S66, T = 25.234 
Q =74° 36' / = 6°57'. 

Carrington (Observations of the Spots on the Sun, Lon- 
don. 1S63) found for the beginning of 1850, Q = 73 40' / = 
7 15'. He represented the varying time of rotation indicated 
by spots at different distances from the Sun's equator by 
means of two empirical formula?, either of which would rep- 
resent his observations tolerably well. These formulae are — 

f = S65' =p 165' s\nh s c = S65' if 165' sin 5 (/— 1°) 

in which / stands for the arc of a meridian of the Sun extend- 
ing from the Sun's equator to that point for which ^ i- re- 
quired. Similar formulae have been drawn up by other 
astronomers. Faye'a (C. lx. 147) is f = 862' — 186 7 sin*/j 
Sporer'^ (N. 1542) is £ = i6°.S475 — 3 -3Si 2 Bin <7-| 41 I 
and Zollner's (N. 1S50) is f = 

northern hemisphere,? = g ■ or£ = ^^ 

for the SunV southern hemisph 

776. Parallax of the Sun. The mean equatorial horizon- 
tal parallax of the Sun (or the equatorial horizontal parallax 



39° Outlines of Astronomy. [Sec. 776. 

of the Sun at a time when its distance from the Earth is 
equal to the semiaxis major of the Earth's orbit) is given by 
recent authorities as follows : — 

Stone, from observations of Mars in 1862 (M. xxxiii. 97), 

3"-94- 

Stone, from the observations of the transit of Venus in 
1769 (Mn. xxviii. 265), S"-9i. 

Newcomb, by the combination of the results obtained by 
a number of methods (YV. p. 29), &'&$• 

Cornu, from his experiments on the velocity of light 
(C. lxxvi. 341), 8".S6. 

From these data it appears that the Sun's parallax is prob- 
ably known to o''.i, but probably not known within o".o5. 

yyj. Distance of the Sun. The trigonometrical tai 
of the Sun's par.dlax is equal to the quotient which would be 
obtained by dividing the equatorial semidiameter of the 
Earth by the semiaxis major of the Earth's orbit. 

The tangent of S'.oo is O.O nearly. 

,, ,, ,, S".S5 ,, 0.00004 j 906 ,, 

,, „ M S"-90 ., O.OOOO43148 „ 

,, ,, ,, 9".oo ,, O.OOOO43633 „ 

The tangents of these small angles are nearly the same as 
the sines of the same angles, or as the ratios of the arcs of 
the same angles to the radius ui any circle to which those 
arcs belong. They therefore increase uniformly with the 
angles, at the rate of 0.000004S4S for cond. Upon 

calculating the semiaxis major of the Earth's orbit (or the 
mean distance of the Sun), by means of the data given al 1 
it will be found that a change of o".o5 in the parallax em- 
ployed makes a difference of over half a million miles in the 
result. It is useless, therefore, to attempt at present to state 
the Sun's distance in smaller units than millions of miles : 
and since all measurements of distances greater than that 
between the Sun and the Earth are based upon this funda- 
mental distance, we see that none of these measurements can 
be stated in smaller units than millions of miles. The mean 
distance of the Sun, by the above data, is accordingly ninety- 
two millions of miles. 



Sec. 778.] Notes, References, and Statistics. 391 

. Dimensions of the Sun. The mean apparent semi- 
diameter of the Sun is 10' 2" (A., Appendix, 4). Twice the 
product of the tangent of this angle (0.0046639) by the Sun's 
mean distance gives us the Sun's diameter, which is reduced 
nearly five thousand miles by an increase of o' / .o5 in the par- 
allax employed. It follows that we may be content for the 
present to state the Sun's diameter in round numbers at 
860,000 miles. 

779. Mass of the Sun. A formula for the number of times 
that the Sun's mass contains the Earth's is given by New- 
comb (W. p. 27) as follows : log Mtt 3 = S.354SS ; in which 
M stands for the required quantity, and n for the Sun's par- 
allax. An increase of o".o5 in the parallax employed will 
diminish the result by about 6,000 ; we can conclude only 
that the Sun's mass is from 320,000 to 330,000 times as great 
as the Earth's. The value of the Earth's mass given below, 
in the list of the masses of the planets, depends upon older 
determinations of parallax than those already quoted. 

780. Periods and Nature of Solar Spots. The period- 
icity of solar spots was discovered by Schwabe. Wolf has 
been the principal inquirer into the length of their periods. 
See numerous papers in the Astronomische Nachrichten, 
especially X. S39. 1043. 1160, 1185, 1199, 1223, 1294, 1420, 
1540, 1577, 1S62. For theories of the constitution of the Sun 
and of its spots at variance with that mentioned in the text, 
see papers by Sporer and by Zollner in the Astronomische 
Nachrichten, especially N. 1542, 1556, 1612, 1835, l $49> J 9^9> 

1974. 

781. Solar Heat. On the subject of the heat of the 
photosphere different astronomers hold very different opin- 
ions, some of which may be learned in the following works. 
(S. 19S-211, 566-584. C. lx. 144- J- 1873, vi. 153. X. 1815.) 

782. Number of Stars. The number of stars visible to 
the naked eye in Germany, according to Heis (Neuer Ilim- 
mels-Atlas, Sternverzeichniss. p. xiii.), is 5.421 ; adding 
proportionate number for the part of the sky not Been from 
Germany, the result is 6,800 for the whole sky. But Gould 



39 2 Outlines of Astronomy. [Sec. 782. 

estimates that 15,000 could be seen if the sky was everywhere 
as clear as it is at Cordoba, in the Argentine Republic. See 
p. 19 of his Address on the occasion of his reception at 
Boston, June 22, 1874. 

783. Variable Stars Algol and Mira. According to 
Schonfeld (N. 1906) the period of Algol is 2 days 20 hours 
48 minutes S3 777 seconds (or about 2.867 days) of mean 
time. When we attempt to determine it correctly within a 
minute, we must take account of the variation of the distance 
of the star which is due to the Earth's motion in its orbit, 
since light requires time to reach us. The following pre- 
dictions by Schonfeld (N. 2001) of the minima of Algol are 
in Paris astronomical mean time, and will enable the reader 
to calculate, for some years to come, the times at which the 
star will appear faint. The difference of longitude between 
Paris (773) and the place lor which the calculation is made 
must of course be taken into account. The predictions have 
been selected so that their times may answer to the evening 
hours of the United States. 

1S74. Dec. 2, I3 h I4 m (in civil time, Dec. 3, i h I4 m \ 
Dec. 22, 14'' 58 m ; 1S75. Jan 14. 13* 31" ; Feb. 3, 15* 16 ' ; Feb. 
26, 13* 50™ ; March iS, 15* 35" ; April 10, 14 s 8™ ; Aug. 17, 
14 1 42'" ; Sept. 9, i3 h n" ; Sept. 29. 14'' 51" ; Oct. 22. 13'' 20" ; 
Nov. 11, I5 h 2 m ; Dec. 4. 13'' 33™ ; Dec. 24. 15* 17". 

A minimum of Mira, according to Schmidt (N. 1988), oc- 
curred Jan. 6, 1874. 

784. Places of Stars. The following table contains the 
mean right ascensions and declinations, for the beginnings 
of 1850 and of 1875, °f ^ ie principal stars named in this 
work. The places of Mira and Algol for 1850 are taken from 
the Catalogue of the British Association, and for 1875 from 
the Vierteljahrsschrift der Astronomischen Gesellschaft. 
The places of the other stars are taken from the English 
Nautical Almanacs for 1850 and for 1S75, m tne ^ rst of which 
north and south declinations are marked respectively N. and 
S., in the second -f- and — . 



Sec. 784.] Notes, References, and Statistics. 393 






- — 

I*, r^ r* - 



— — J 



l-H-H + l MIN I I I | + | I+++I 



— -. Is C Q — Q • - 3 ' N ~ - ♦ C 



--.—-,-—;;; . - - 



-.X -T f 



n - 



I C X t^X DC • 



r^ t^ r^ 






n>C »>"> n n 



no<o woe st e n mosnss n 

fe H fc r. s.y s Z j. 



- : 

- ■ 

— _.- |l)tq n n — ■ ». « ^- N — ir. ft — N 



r, C C t^ I - 



5 ^ 




- 






1 


r 




1 1 1 



. . . 

r (a i -'ni.iiii 11.... 






- 

- 
< 

r 









~ - - — — 



394 Outlines of Astronomy. [Sec. 785. 

785. Data relating to the Places of Stars. The yearly 
amount of precession for 1800 is 50". 241 1 ; and it is now 
yearly increasing by o" . 0002268. Hence for 1850 it is 
50". 2524 ; for 1875, 50". 2581. The mean obliquity of the 
ecliptic for 1877 (or its obliquity when we disregard the effect 
of nutation) is 23 27' 18". 46 ; it diminishes at present by 
o // .i272 in 100 days ; hence for 1875 ]i is 2 3° 2 7' l 9"'39- The 
constant of aberration (or half the greatest difference, due to 
aberration, between two of the apparent places of any star) is 
20 /, 445l. (A. 248; Appendix. 3.) 

The change in the right ascension and declination of a star 
occasioned by precession vary according to its place as well 
as with time. For 1877, the yearly changes are as follows: a 
standing for right ascension and d for declination. The in- 
crease in a is 3'. 07 2 29 -j- i'.33^>93 sin a tan 8 ; that in 8 is 
20 // .054o cos a (A. 258). The angles having at the beginning 
of 1877 the values i". 33693 and 20". 0540 are equal (405). 
Their decrease in ten years is at present o*. 00006 or o^.CKXX). 
The angle having at the beginning of 1S77 the value 3'.07229 
is now increasing at the rate of o'.ooo20 in ten years. The 
student who his any knowledge of trigonometry will perceive 
that the right ascensions of most, but not of all, stars inert: 
by the effect of precession ; while if we consider a northward 
movement as an increase of declination, precession increases 
declination in half the celestial sphere and lessens it in the 
other half. With the data already given, we may calculate the 
precession in n and fi of any s'tar in our list for any time not 
very remote. For example, let us calculate the effect of pre- 
cession on the star Arcturus from 1850 to 1875. As its a 
and fi are constantly changing, and yet are required in the 
calculation, it will be best to take them half-way between 
1850 and 1875. ^e can do this at once by means of the 
list ; if we had the star's place given for some one date only, 
we might begin by using that place in a rough calculation of 
its place for 1862^ (or the middle of 1862). We have from 
the list, for 1862^, a = I4 h g m 23 s , or 212 21', which is suffi- 
ciently accurate for our purpose ; d = -\- 19 54'. The yearly 



Sec. 785.] Notes, References, and Statistics. 395 

increase of a, for 1862^, appears from the data given above to 
be y.072 -\- I s . 337 sin a tan S, and the yearly increase of fl to 
be 20". 05 5 cos a. The computation will accordingly be as 
follows : — 






log 1-337- • • 0.12613 Log 30.355. . 1.30222 

log Bin 212° 2\ f 9 7-S43 log COn 212° 2l' 9.92675 

log tan 19° 54' . 9.55870 



9.41326 1.22897 

By the rules of trigonometry, the numbers corresponding 
to the logarithms just obtained are both negative. The right 
ascension of Arcturus was therefore yearly increasing, at 
the time 1862 J, by 3'.o72 — o\259, or 2 '-$ l 3 > * ts declination, 
at the same time, was yearly diminishing by 16". 94. Hence, 
between 1850 and 1S75, i ts right ascension increased about 
70'. 325 and its declination diminished about 423". 50. If 
Arcturus had no proper motion, these differences would 
nearly answer to the change in its mean place (562) 
between 1850 and 1S75. The actual differences, from the 
list, are 68*429 and 472 7/ .42 ; we find, then, that during 
twenty-five years the star's proper motion diminished its 
right ascension (or made it retrograde) about i 8 -9, and 
carried it southwards nearly 49". This is a large proper 
motion compared with that of most stars. During the last 
two thousand years, Arcturus must have changed its appar- 
ent place among the other stars more than a degree. 

786. Examples of Binary Stars and of Stellar Parallax. 
The places of the stars named in this section hav< _iven 

, above, except those of ( Herculis, £ Ursae Majoris, and 61 
^ni, the approximate places of which for [875 arc res 
35'- + 3i° 5°' ', u b n rn 3r. + 32 14 ; 2I h I' 
+ 3S 8'. When two or three periods of revoluti iven 

for a binary star, they show how nearly the results 1 
ent inquirers agree. A parallax of \" ansv 

m us of 206,265 times the semiaxis maj rtlTa 

orbit ; and as the angles of parallax are so small that their 
arcs may be taken for their tangents, the S of two 

stars are inversely as their parallax 



39 6 



Outlines of Astronomy. [Sec. 786. 



Name. 


Period in years. 


Parallax. 


Authentic 

ferred to. 


C Herculis . . 


30.216, 34.57, 36.357 





O. 61 5 


f Ursae Majoris 


58.262, 60.60, 61.576 




426. 
O615; Mn. xxxiv. 

M.xn. 


a Centauri . . 


7700, 81.40 


o // «9 to i^.o 
















169. 


a Geminorum . 


252.66, 632.27 

rhit ; ) 
J only a d.t- 1 







61 Cygni . . 


Over 500 \ ference 0! > 


Under o".4 


1 ; N. 




| proper mo- 




.1 1) z u ng»- 




( lion. 




Heil 


Sirius . . . 


49.418 


About o/ f .2 


. v. 6 ; 
Mn xxv. 39. 


Vega .... 




About of f .2 









787. Elements of Planets and Satellites. A full 
meat of a planet's movement about the Sun, or that of a 
satellite about its planet, includes — 

I. The number of days of mean time in which the moving 
body makes one 6idereal revolution; or. which will serve a 
like purpose, a number of seconds of arc, the product of whi 
by that number of days i^ 1,296.000 (the number of seconds in 
the whole circle). This is called the mean motion of the 
moving bodv, or its mean daily motion, and is often denoted 
by fi. Sometimes the mean yearly motion of the moving b< 

is used as one of its elements. This mean yearly motion is to 
the mean daily motion as one Julian year of 365! days is to 
one dav. It is often denoted by ;/. 

II. The ratio of the semi ax is major of the planet's orbit to 
that of the Earth's orbit. This is usually denoted \ 

III. The ratio of the mass of the planet to that of the Sun. 
This is denoted by m, 

IV. The eccentricity of the planet's orbit. This is denoted 
by e% or by e. 

V. The heliocentric longitude of the planet's perihelion, 
denoted by n. 

VI. The heliocentric longitude of the ascending node of the 
orbit, often denoted by Q , sometimes by 0. 



Sec. 787.] Notes, References, and Statistics. 397 

VII. The inclination of the plane of the orbit to the plane 
of the ecliptic, denoted bv /, 1. or o : the symbol is frequently 

ed in a different sense, to denote the angle, the sine of 
which is <?. 

VIII The date (usually called the epoch) for which ele- 
ments IV.. V . VI., and VII., have bren calculated 

IX. The mean anomaly, denoted by M, of the planet itself 
at this epoch: or an angle equal to the sum of M and -, and 
called the planet's mean longitude. This angle is denoted by 
L, /. or sometimes e. 

These nine data are not always enumerated in the same 
order, and may be reduced to seven by omitting the mass 
(which is necessary in the case of an asteroid or comet), and 
taking the epoch at the time of the planet's perihelion pas- 
sage ; this is customary in calculations of the orbits of 
comets, and makes the element L or M superfluous. If 
a comet is supposed to move in a parabola, the element e 
becomes equal to unity, and disappears from the list of 
elements. The orbit is then easier to compute ; and for this 
reason a comet is always supposed to move in a parabola, if 
a parabolic orbit will satisfy the observations. Since a is 
infinite in a parabolic orbit, it is replaced by q, the distance 
from focus to perihelion, in terms of the semiaxis major of 
the Earth's orbit. 

788. Approximate elements of the eight principal 
planets, by Le Verrier (P. ii. 58 to 62) are given on the fol- 
lowing page. The epoch is mean noon, Jan. 1, 1850, with 
the mean equinox and ecliptic of that date. 

789. Corrections to these Elements. Le Verrier found 
that the elements of the Earth adopted at the outset of his 
investigations, and here quoted, required the following cor- 
rections (P. iv. 52. 53. 97 to 104) : it should be diminished 

i3".5: /increased by 7". 39 ; * increased by 0.00000c; 
and the mean yearly motion, ;/ (derived from the time of 
the sidereal revolution), increased by o".o6o3. The solar 

llax previously accepted (8". 57). and the received ra 
of the Earth, were shown by this investigation to be too 



393 



Outlines of Astronomy. [Sec. 789. 



Name. 


Period in days. 


m 


a 


' 


Mercury . . 


8 7. 9^92 5 80 


, 


0.3870987 


0.205 


3,000,000 


Venus . . 


224 7007869 


i 


0.7233322 


0.0c. 


401, 


Earth . . . 


365.2563744 


35 t. 


1. 0000000 


0.01677046 


Mars . . . 


686.97 


■ 


1. 523691 


0.09; 1 


2/>8o,33 7 


Jupiter . . 


4,332-5 




5.2. 1 


0. 048a 


Saturn . . 


io>759«*> 


1 


9-5 v 


0.055 


Uranus . . 




1 
. 00 




0.04' 


Neptune . . 




1 
1 i,i'.> 




o.oo v 


Name* 


n 


+ 





/ 




O / // 


/ // 


/ // 


O / // 


Mercury . . 


75 7 


7 ° 


1 3-25 


327 if 


Venue . • 


I 5 r > ° 


I 23 


75 If 4 >5 


245 33 '4-4 




100 21 40.0 
333 17 50-5 






100 4' 
S3 40 5a 6 


Ifan • • • 


1 51 5.0S 


4S »| 


Jupiter . 


11 54 J v 1 


1 iS 


H 2°-45 


160 1 20.3 


Saturn . ■ 


90 6 12.0 


2 29 


112 si 


14 50 40.6 


Uranus . . 


' 45 


46 


73 14 14.35 


28 26 41.5 


Neptune . . 


47 M 37*3 


1 «6 


130 6 51.58 


335 8 58.5 



small, unless a group of asteroids was supposed to exist near 
the orbit of the Earth (P. vi. 187). 

Le Vomer's corrections to the elements of Mercury are as 
follows (P. v. 107): it should be increased by 13". 93 ; /by 
o"-53 ; by 5". 50 ; c diminished by 0.00001312 ; <f> by o".45- 
The corrected mass of Mercury is g^m °f tne Sun's (P. vi. 
92). 

The corrections to the elements of Venus are as follows 
(P. vi. 95) : 7T should be increased by 3' 18". 5 ; /by a". 30: 
6 by 48".! 5; (j) by 4 ;/ .o8 ; e by 0.00000991; ;// reduced to 
4i^o (P. vi. 309). 



Sec. 7S9.] Notes, References, and StATisncs, 399 



For Mars (P. vi. 309), tt should be increased by 3". 1 7 ; 
6 by 68". 35 ; * diminished by 0.00000047 : / by lo/'.27. The 
mass of Mars must be diminished by about one-tenth (P. iv. 
96). 

The total mass of the asteroids is at most not much over 
one-third of the Earth's mass (C lii. 11 11). 

Newcomb's elements of Uranus and Neptune, for mean 
noon of Dec. 31, 1849, Greenwich time, are as follows (pp. 
184, 31, 53. of his Investigation of the Orbit of Uranus, pub- 
lished by the Smithsonian Institution, 1873) '• — 





n 


m 


a 


e 


Uranus 
Neptune 


ft 

I5424-797 

7S64.935 


1 
•00 

1 


19 if 

30.0705 


0.0463592 
0.008 . 




V 


<*> 





1 


Uranus 
Neptune 


43 17 3o 


0° 46^ 20 // .92 

r 47 1.6 


73° 14' 3/ 7 .6 

130 7 33 


29 i2 r 43". 73 

335 5 39 



Lehmann's elements of the eight principal planets for 1800 
(N. 1748) may also be consulted; but it has already been 
sufficiently shown that, with the exception of the masses, the 
elements first quoted admit only of small corrections. 

790. Variations of Planetary Elements. To show the 
rates at which these elements change, the values of c, 7r, $, 
and By 10,000 years before and 10,000 years after 1800 (P. ii. 



ies. 


e 


n 


* 


e 






/ 





/ 


ft 


r 


Mercury .... 


1 

I 0.2056 




7 
6 


' 1 
42 


50 


57 
34 


Venus 


( 0.0129 
Jo.- 


no 1 


3 


6 


21 


99 

47 






3 


2 


O 


rth 


( 0.0187 
| 0. 




1 


24 








134 '4 


1 


'4 







} 0.: 


'5 


2 


27 


51 


70 

7 1 











'" 



400 Outlines of Astronomy. [Sec. 790. 

Additions, 29), are given at the foot of the preceding page for 
Mercury, Venus, the Earth, and Mars. The equinox and 
ecliptic are those of 1800. 

The eccentricities and inclinations of the orbits of the 
planets are confined within narrow limits. For instance, the 
eccentricity of the Earth's orbit was 0.0473, and its inclina- 
tion (to the plane of the ecliptic for 1800) was 3 45' 31" , 
at a time 100,000 years before 1800. The eccentricity has 
been diminishing ever since, and will go on diminishing for 
23.980 years, amounting then to 0.0033 5 it will afterwards 
increase (P. ii. 153). The inclination of the Earth's orbit 
(P. ii. 163) to the plane of the ecliptic for 1800 can never be 
as much as 5 . 

Another recent investigation of the changes in the plane- 
tary elements which require very long periods of time for 
their completion, and are hence called secular variations 
StockwelPs Memoir on the Secular Variations of the Elements 
of the Orbits of the eight principal Planets, published at 
Washington, in 1S72, by the Smithsonian Institution. The 
introduction to this work contains, among others, the follow- 
ing statements. The equinoxes perform a complete revolu- 
tion in the heavens (by reason o( \ n) in the aver 
interval of 25.694.S years ; but on account of the secular 
inequalities in their motion, the time of one of their revolu- 
tions may differ from this amount by 2S1.2 years. The max- 
imum variation of the tropical year is equal to 10S.40 seconds 
of time. The limits of the obliquity of the apparent ecliptic 
to the equator are 24 35' 5S" and 21 58' 36" ; whence it fol- 
lows that the greatest and least declinations of the Sun at 
the solstices can never differ at different times more than 
2 37' 22". The eccentricity of the Earth's orbit varies from 
nothing to 00693SSS. 

791. Examples of the elements of asteroids, derived 
from the Berliner Astronomisches Jahrbuch for 1876. The 
mean distance of Flora is less, and the inclination of the 
orbit of Pallas to the plane of the ecliptic is greater, than that 
of any other asteroid yet discovered. The asteroid having 



Sec. 791.] Notes, References, and Statistics. 401 



the most eccentric orbit is No. 125 in order ot discovery; it 
has not been named, and its orbit is not known well enough 
to allow its place to be predicted accurately ; but as other 
asteroids have orbits nearly as eccentric, it will serve as an 
example. The asteroid having the greatest mean distance is 
Camilla. Like No. 125, it has escaped the observation of 
onomers tor some time past, and its orbit cannot be said 
to be well known ; but the mean distances of some other 
asteroids are not much less than Camilla's. Of the two 
epochs given for Xo. 125 and Camilla, the second is that of 
the mean equinox used in the computation; for Flora and 
Pallas, the epochs of the equinox and elements are the same. 



N me. 


Epochs. 


M 


a 


e 


Flora 

is . . 
1 as • 




Jan 1. 

■ 1 v 7 4 • 
12. 1873. 

j 


ff 
670.09 


2 2014 
2.7716 

3-°35 2 
3-5602 


0^670 
0.23*47 

o-34^75 
0.12272 


1 Name. 


V 


i 


Q 


/ 


r .or;* . 
Pal as . . 
N 
Camilla . 


/ tr 

32 ? * - 
i a i 53 : 

251 10 25.0 
"^ 4 y S 


/ /y 

5 53 3.o 
34 4' 

6 4 

9 47 4i 5 


/ // 
1 10 1 - 

171 9 42-0 
1/5 41 20.3 


/ // 
68 4 « |I4 

*7 3 4 54 6 

315 55 54 

55 57 3-6 



Distances and Synodical Revolutions of Planets. 
From the preceding elements may be derived the greatest 
and least distances of each planet from the Sun and from the 
Earth, and the period of its synodical revolution. In order 
that Mercury or Venus should be as near the Earth as pos- 
sible, it must be at one of its nodes, in aphelion, and at its 
inferior conjunction, at the moment when the Earth is in 
perihelion. In order that it should be as far as possible 
from the Earth, it must be at a node, in aphelion, and at its 
superior conjunction, at the moment when the Earth is in 
aphelion. In order that a superior planet should be as near 

26 



402 



Outlines of Astronomy. [Sec. 792. 



the Earth as possible, it must be at a node, in perihelion, and 
in opposition, when the Earth is in aphelion ; and in order to 
be as far as possible from the Earth, it must be at a node, in 
aphelion, and in conjunction, when the Earth is in aphel 
These combinations of circumstances can seldom or ne 
happen ; the distance of a planet from the Earth at any par- 
ticular conjunction or opposition must be calculated, if it is 
required, from the places of the planet and of the Earth at 
the given moment. We will take the Earth's mean distance 
from the Sun at 92 millions of miles, as above ; its greatest 
distance will then be about 93.}, and its least distance about 
90^, millions of miles. 

The problem of finding the synod ical revolution of any 
planet from that of its sidereal revolution is of the same sort 
with the question, repeated in most collections of algebraic 
or of arithmetical examples, "How long after 12 o'clock 
are the two hands of a clock again together?" Its solution, 
therefore, may be left to the student ; but the approximate 
synodical periods of the planets, as well as their approximate 
sidereal periods, are given in the following tables. The 
years are Julian years of 365 J days each. The distances are 
stated in millions of miles, but must not be supposed to be 
known accurately. 



£ p 



rt 5 3 

o 



Name. 



Mercury 
Venus 
Earth . 
Mars . 
Flora • 
Pallas 

Camilla 
Jupiter 
Saturn 
Uranus 
Neptune 



Sidereal period. 



Years. Days. 
o 88 



3 

4 

5 

6 

11 

20 

84 

164 



322 
97 
224 
i°5 
262 

3i5 

107 

6 

226 



43 

67 1 
93* 

,5 T 
234* 

315} 

376 

367} 

501} 

926f 

2787* 



i_ f. 

- 



66 
9o* 

127 
170: 1 

2739 ; 



Sec. 792.] Notes, References, and Statistics. 403 






Mercury • 
Venus 

Camilla . 
Jupiter . 
Saturn 

Neptune . 







1 - 


- - 






















. 




Synodica 


period 


























O 


- 


\\ us. 


P. IV-. 









ii'. 




47I 


1 


219 




2.4 


2 


i 1 






1 


toi 




::\ 


1 






1 


&5 




B9 


1 


34 
13 


46i| 


735 


1 


■ 


4 


lc;4oi 




1 


2 




20452 



27^ million miles. 



Greatest distance of Venus, at inferior 

conjunction, from the Earth .... 

Greatest distance of Mars, at opposition, 

from the Earth 62J ,, ,, 

Hence Mars may be nearly twice as far from the Earth at 
I one opposition as at another. 

793. Bulk and Density of Planets. The bulk of a planet 
may be readily calculated when we know its distance and 
apparent diameter : and its density may then be found from 

bulk and mass. But as we have seen, the masses of the 
planets are not precisely determined ; their distances depend 
on the Sun's parallax, our knowledge of which is still unsat- 

ictory ; and their apparent diameters must be obtained 
from measures of their disks, which are difficult to execute 
with precision, as will appear by the following figures, col- 
lected by Kaiser (L. 213 to 274). The apparent diameter of 
Mercury, at a distance equal to the semi axis major of the 

rth's orbit, ranges, according to different observers, from 

2 to 6". 9 ; that of Venus from i6".6 to 17". 9: the apparent 
ial diameter of Mars from 9". 6 to 9^.2 ; its appar- 
ent polar diameter from 9". 4 to 9". 2. Similar disagreements; 
appear in different estimates of the apparent diameters of 
Jupiter, Saturn. Uranus, and Neptune, at a distance for each 
planet equal to the semiaxis major of its orbit Tims the 
equatorial diameter of Jupiter ranges from 3/'. 5 to 37". 1 ; its 



4°4 



Outlines of Astronomy. [Sec. 793. 



polar diameter from yj' '.9 to 35". 1 ; the equatorial diameter 
of Saturn from 18". 5 to 16" 9 ; its polar diameter from 1CV.8 
to 15". 1 ; the diameter of Uranus from 2 h '.9 to 3". 6 ; that of 
Neptune from 2". 5 to 4" 4. The polar compression of Jupi- 
ter, according to different observers, ranges from fa to *^ ; 
that of Saturn from ^ to ^ ; tho.se of other planets cannot as 
yet be said to he even approximately known : and different 
measurements of Saturn's ring differ enough to make ei 
statistical statements of its dimensions somewhat illus 
The following table will give some notion of the bulk and 
density of the planets as compared with the Sun and with the 
Earth. It has been formed from approximal ;.t diam- 

eters derived from the figures just quoted, the Earth's 
ent diameter at its mean distance from the Sun being 17". 8, 
or twice the solar parallax S '.<;. The m : the pla: 

have been corrected by the data already -iv 



Name. 



Sun. 



Mercury 
Venus . . 
Mara . 
Jupiter 

Saturn 

Uranus . 

Neptune . 















V z - 



// 

3 
6 

>7 

43. 1 



Z 









320,000 
0.06 

0.1 1 
305 
91 






0.25 
008 



The student only needs a knowledge of arithmetic, and of 
the facts contained in this book, to enable him to construct 
similar tables for other values of the apparent diameters of 
the planets ; since these angles are so small that their arcs 
may be used for their tangents. The ratio of the bulk of one 
globe to that of another may be expressed by the ratio of the 
cubes of the diameters of the globes. It will be found that the 
relative densities of the planets will vary considerably accord- 
ing to the diameters which may be used in the calculation. 



Sec. 794.] Notes, References, and Statistics. 405 

794. Rotation of Planets. The time of rotation of Mars, 
according to Kaiser, who regards it however as not yet de- 
termined to the tenth of a second (L. So), is 24 h 37™ 22\G 
mean time (L. 76, jy). According to Schmidt (X. 1^65), 
it is 24 h 37 tu 22\6o3. Proctor's value is 24*' 37™ 22*735 
(Essays on Astronomy, Appendix A). The period of 
Jupiter's rotation, according to various observers, rang! 
from 9 h 50 m to 9 h 56 m (N. 1973); it varies to some extent 
according to the part of the disk which is observed ; see 
Lohse's paper in Vol. II. of the Bothkamp Observations, 
Leipzig, 1873. W. Herschel found that Saturn's rotation 
occupied io h i6 m (H. 1794) His value for the inclination of 
the axis of Mars to the plane of that planet's orbit is 6i° 18', 
according to which the obliquity of the ecliptic of Mars is 
28 42' (H. 1784). The exact determination of the poles of 
Jupiter and Saturn has not been found practicable. 

795. Satellites. The following numbers relating to the 
satellites (except the Moon's apparent diameter) have been 
derived from the tables in J. J. von Littrow's u Wunder des 
Himmels," fifth edition, revised by Karl von Littrow, and 
published at Stuttgart in 1S66. This work gives the original 
authorities for its statistics. 

Sidereal revolution of the Moon, in mean 

time 27 d 7 h 43 m n'-s 

Svnodical revolution of the Moon, in 
"mean time 29 12 44 2.9 

Eccentricity of the Moon's orbit . . .005490807 

Inclination of the Moon's orbit . . . • 5° S' 39 '.96 

Inclination of Moon's equator to the 

ecliptic i° -S' 25" 

Tropical revolution (revolution with re- 
spect to the vernal equinox) of the 

e 8.S473 Julian years 

Tropical revolution of the Moon's nodes 
f period of Earth's lunar nutation and 
tropical period of Moon's precessional 
movement) 1S612S ,, »» 



406 



Outlines of Astronomy. [Sec. 795. 



Mean equatorial horizontal parallax of Moon . . 
Mean distance of Moon, in equatorial diameters of 

the Earth 30.1389 

Ratio of mass of Moon to Earth's mass .... ^ 
Ratio of apparent semidiameter of Moon to its 
equatorial horizontal parallax (by Pence's tables 

of the Moon) 0.272:74 

Unless we wish to be very accurate, we may take the List 
ratio for that between the Moon's actual diameter and the 
Earth's. 

The following table, under the heading "Distance," con- 
tains the ratio of the mean distance of each satellite from its 
primary to that of the Earth from the Sun ; under the head- 
ing " Inclination," the angle between the plane of the satel- 
lite's orbit about its planet, and that of the ecliptic, except for 
Jupiter's satellites ; the inclinations of their orbits here given 
are inclinations to the plane of Jupiter's orbit. The column 
headed ki Period " contains the period of the sidereal revolu- 
tion of each satellite about its planet, stated in days of 
mean time. The apparent diameters of Jupiter's satellites are 
respectively P'.oij, o".9ii, l".4S8, l".273, at the Earth's 
mean distance from Jupiter ; these measurements are liable, 
of course, to considerable inaccurai 



Name. 


1 faUnce. 


Inclination. 


Period. 




(I 


0.002S19 

O.C* i 

0.00 

0.01. 

0.00124 

0.00159 

0.00197 

0.0. 

0.0 

0.0 

o.o< 

0.02 3 So 

0.00138 
0.00192 
0.003 1 5 
0.00420 

0.00237 


3° 5' MP 

3 4 25 
3 

2 40 58 

Uncertain. 
' tin. 

1 ' 

2S IO 

' 47" 

I ncertain. 

Uncertain. 
Uncertain. 

ioo° 3/ 
100 34 

i 5 o° 


o.<>42 
4.517 

2.520 
8.706 


Satellites of Jupiter 


11. . . . 

1 III. . . 






iv. . : 




Satellites of Saturn ■ 

Satellites of Uranus- 
Satellite of Neptune 


Mimas 
Enc ladus 
Thetis . 

Dione 
Rhea . . 
Titan . . 
Hyperion 
, lapetus . 

Ariel . . 

Umbriel . 

Titania . 

, Oberon . 







Sec. 795.] Notes, Referenxes, and Statistics. 407 

The satellites of Uranus have retrograde movement around 
it ; hence their inclinations are set down at ioo° 34' instead 
of 7<f 26' '. The satellite of Neptune also probably retrogrades, 
and its inclination is therefore 150° instead of 30 . 

796. Incandescence. According to Draper (J. 1847, iv. 
3S8) the shining of an object at a less heat than 977 degrees 
Fahrenheit is to be considered phosphorescence rather than 
incandescence. When a solid or liquid body is gradually 
heated, the first light which it emits on becoming incan- 
descent is red, and the body is said to be red hot. The 
light of phosphorescence is usually bluish or greenish. 

797. Ether and Atmosphere. It is generally thought 
that no space is absolutely empty. Some philosophers hold 
that gases like those which constitute the Earth's atmosphere 
exist in a highly rarefied condition throughout the universe 
(Z. 92). In this case, these gases may perhaps be regarded 
as constituting the medium which transmits to us the light 
of celestial objects and is called the ether (C. xxxix. 529). 
Zollner considers it probable that the absence of any percep- 
tible atmosphere about the Moon is due to the smallness of its 
mass, and that the small mass of Mercury favors the supposi- 
tion that it has no atmosphere. On these principles the atmos- 
phere of Mars cannot be chiefly composed of gases like the 

D and nitrogen of our atmosphere (Z. pp. 102 to 105). 

798. Numbering of Comets. Chambers, in the list of 
comets in his Descriptive Astronomy, arranges them by their 
perihelion passages ; but Donati's Comet (for instance) is 
usually called the fifth of 1858 rather than the sixth, as it 
would be by order of perihelion passages. 

799. Example of the Elements of a Comet (X. 2003). 
Mean Berlin time of perihelion pas-au r e, 1S74. July 8.S93S5. 
Longitude of perihelion 27 1° 6' io/'-.O 

Longitude of a-cending node nS 3 

44' 2; ".3 f mean equinox, 1S74.0 

Inclination of orbit to ecliptic 66° 20' | 

J 

Eccentricity. 0.99S72. Semiaxis major, 529.51. 
Period of revolution, 12,184.3 years* 



408 Outlines of Astronomy. [Sec. 799. 

This comet was the third of 1874, usually called Coggia's 
Comet, from its discoverer. If the elements just given are 
correct, the comet will return when Vega is the North Star 
(168). 

800. Tropical and Anomalistic Years. The yearly 
amount of precession being 50 J'' (785), the tropical year is 
less than the sidereal year by the time in which the mean 
motion of the Earth in longitude amounts to 50^-". In other 
words, the tropical year is to the sidereal year (788) as 
1,295,949;} is to 1,296,000, the number of seconds in 360 . 
The tropical year is therefore about 365.2422 days of mean 
time. 

The yearly advance of the apsides of the Earth's orbit is 
about u".8 (O. 243) ; the anomalistic year is therefore about 
365.2597 days of mean time. 

801. Illumination of Dark Side of Venus. Gruithuisen's 
fanciful hypothesis on this subject (343) may be found in his 
" Astronomisches Jahrbuch .... fiir das Jahr 1842," p. I 
note. 

802. Height of Shooting Stars and of Auroras. On 
these subjects, see J. lS68, xlv. 235 ; N. 1 58 1, 1662 ; J. 1865, 
xxxix. 286; 1871, i. 128; 1S72, iii. 273. 

803. Variability of the Earth's Rotation. See Thomson 
and Tait's Treatise on Natural Philosophy, Vol. I. p. 686, 
on the retardation of the Earth's rotation by tidal action ; 
and Newcomb on the variability of the rotation (J. 1874, 
viii. 161). 

804. Optical Theories. Van der Willigen has lately writ- 
ten a paper on the unte liability of the opinion that the m< 
ment of a luminous body or of the prism through which it is 
observed can affect the refrangibility of its light. The paper 
has been published in French. The Dutch version is in the 
Verslagen en Mededeelingen der K. Akademie van Weten- 
schappen, Afdeeling Natuurkunde (for 1873). 

Recent experiments by Draper (J. 1872, iv. 161 ; 1873, v. 
25, 91) have apparently disproved the formerly prevalent 
theory of three spectra (495). 



Sec. S05.] Notes, References, and Statistics. 409 

805. Mean and Sidereal Time. If we know the places, 
at a given moment, oi the hands oi a clock set to either of 
these kinds of time, we can find the corresponding places 
of the hands ot a clock set to the other kind of time, by 
means of the data given in all large almanacs. These data 
include the mean times o\ the upper culminations o( the 
vernal equinox, or the sidereal times of mean mum, for some 
given meridian : and as these times change from year to 
year, they cannot be given except for some particular year. 
Hence, in order to rind them, the almanac must he con- 
sulted. 

Form of Orbits under the Laws of Gravitation 
and Inertia. The following statements aie from Price's 
Treatise on Infinitesimal Calculus, Vol. III. (Oxford. [856), 
pages 47S. 4S0, 4S5. Suppose a particle to be projected with 

/ven velocity from a given point and in a given line : and 
to move under the action of an attractive force which is 
always directed towards a second given point, and varies 
inversely as the square of the distance between the point to 
which it is directed and the moving particle. According as 
the velocity with which the particle was projected is less 
than, equal to, or greater than, that which would be acquired 
by the particle moving from an infinite distance, under the 
action of the attractive force, to the point from which it was 
projected, so will its orbit be an ellipse, a parabola, or a 
hyperbola, with the centre of force in the focus. In this 
statement, the circle is regarded as one kind of ellipse. If 
the particle is projected from an apse with a velocity such 
that the centrifugal force is equal to the attractive force, the 
orbit of the particle is a circle. 

807. Times of High and Low Tide. The: omet- 

rical demonstration by Airy (Mn. xxvi. 22.S) that the cor 
quence of the constant change of place of any part of the 
rth with respect to the I suppose the ocean to 

occupy the equatorial parts of the Earth's surface and the 
water to move without friction), would be to make it al\\ 
low water under the Moon, so that each high tide would 



410 Outlines of Astronomy. [Sec. 807. 

come a quarter of a lunar day after one of the Moon's culmi- 
nations. In fact, as we have already seen (674), there is 
often a still longer interval between the times of the Moon's 
culmination and of high tide. 



INDEX. 



The references given in this index are to the sections of the preeedirg work. 
ch page will be found the number of the section to which its hist 
line belongs. 



Abbreviations « f titles, 771. 
Aberral 

Actink . 
Adam-. 

;, ^44. 
.11. 

wre. 
^07. 

Alphonso, Alphonsir.e Tables. 707. 

Altitude and azimuth instrument, 595. 

Amount of motion, 605. 

Amplitude, 520. 

ng spectroscope, one in which 
an im.ige of the object observed is 
formed upon the slit, so that the light 
passing the slit comes only from part 
of the object. Set 

tros 

-, 688. 
\r distance. 
Annular 

; - >8. 
Anomalistic revolution, 335, 568, 800. 

2 1 6. 
Aperture, 4 
Aphelion, 146, 228, 241, 564, 792. 

Apogee 

ent movement, in, 123, 134. 
Apparent pin 
Apparent tin 
Apside 

. 681, 706. 

410. 
Arctic. 167. 295. 

700, 701. 

- 

•mical time. 

rth and other 
bode 



Attraction, 608, 671, 712. 
Augustus, 

Automatic S| . ; 03. 

Axis, J3 to 35, 145. «5 S - i&5 to I_ 

» 403 to 417, 531 J axes of instru- 
ments, 591 to 59S. 
Azimuth, 520. 

Bailv's 1 

17, 618, 66S, 718. 
Bayer, 

Belts of Jupiter and Saturn, 205, 209. 
Bessel, 746, 747, 772. 
Binary stars, 91, 661, 725, 7S6. 
Bode's Law, 203. 
P.odies, 5. 

Bolides ; large shooting stars. See Fire- 
balls. 
Bradley, 739, 746. 
Bridges (of solar spots), 57. 
Brightness of distant objects, 457, 458. 
Bunsen, 749. 

Czesar, 755. 

Calendar, 70?, 755 to 757. 
Camera, 444. 
Carrington, 775. 
, 729. 

. 682 to 685, 694. 
Cavendish experiment, 663. 

alt 4« 

■.'. perspective, 266. 
I !al spline, 51 1. 
Centre, 145, 157, 409, 412. 
Centre of gravity, 34, 44, 638, 666. 

e 

ical differences, 9, 498. 
Chromosphere 
Chronogra] b, 5-0 ; 
Chroi 

Aid fol- 
low! T 

Circumference, 409. 

.•72. 
Civil time, 315. 
Clarke, 772. 



412 



Index. 



Clepsydra, 704. 

Clocks, 310, 311, 543, 544, 547, 579 to 
5^3, m- 

Clusters, 89, 223, 226. 

Coincidence, 3^4. 

Colors, 15, 96, 104, 425, 492, 495- 

Colures, 5O5, 566. 

Coma, 231. 

Comets, 2S, 228 to 240, 643, 798, 799. 

Common, 392, 42 j. 

tnio is, component . 
Composition of movements, 115. 

I M- 

Continuous spectrum, . 
Convexj 

mcus, 709. 

I76» 373* 
Corn 1, 739, 742, 
Crab 
1 

, 690, 695. 
1 

191, ',.1 to 

Di imeter, . 793. 

1 

D •. 155, 

• \ - • 1 » > 

l>isk. 1 

I ] ! • 
1 1 : ince, 24, 79, 
rtion, 444. 
Diurnal movement, 524, 596, 689, 690. 
Divergent, i.;i- 
I lollond, 725 

I >oul 786. 

Down, 253. 
Draper, 

Earth, 1 to 4, 19 to a?, 35 to 
105 to 175, 248 to 25 s 254 to 21 

East, 124, 15 . 

Eccentric. 34. 

Eccentricity, 145. 

Eclipses, ?h j 29i J47j 564 to 388, 440, 

504. . 5 >5i 7°*i 75»- 
I LptlC, 322, 531, 549, 693, 7S5. 
Egypt, 679, 
Egyptian year, 750. 
Electricity, 14, 272, 58010582. 
Ellipse, 145. 



Elongation, 332. 
Emersion, 362. 
Empirical laws, 1 1 7. 
I 766, 768. 

Ephemera, 70^, 771. 

Equal it . 

Equation ; this word is often used by 
astronomers in the sense of difference, 
or correction. The equation 
is the difference at any moment be- 
tween mean and true time. 

Equator, terrestrial and celestial, 40, 

1 

Equilibrium, 

Equin< 

Equinox, 297, 301 to 304, 309, 323, 533, 

l.qui 
Ether. 

g and inon.; 

Eye-pu 

I 

. 487. 

I • 533- 

469. 
'45. 445 

.r.\ S, 117. 
• 514- 

^34' 

tated circle^. 
Granule 

( rreat circles, 412. 

( ireeory XIII., < Iregorian calendar, 756. 
Gruithuisen's conjecture respecting in- 
habitants of Venus, 343. 
( ryroscope, 133. 729. 

Halle- 

Halo. 270. 

Harvest and hunter's moons, 341. 



I-VDEX. 



413 



Headway, 2, 601, 621. 

: ;. -4, 97, 192, 261. 

mtric, 514. 

Hem 166. 

Hendei 

Herschel, J. F. W 

Hc\ 

Hookc . 

■n. horizontal, 255, 204, 516. 
Horrocks. 731. 
Hour 

Hours 750. 

5, 103, 497 to 499. 
Hypei; 

^ to 44S, 467 to 482, 598. 
Immersion, 362. 

796. 
Incidei :•.. 

Inertia. (x>i, 614, 622. 
Inferi i 
Intii 
Inhab::. estial objects, 19, 343, 

:;ng spectroscope, a spectroscope 

so arranged that the light reaching 

the slit is composed of parallel pencils 

the object observed. 

cope. 

Intersection 4 12. 

480. 
brad 

§64, 3^5' 
660, ' 

Julian year and period, 755, 792. 

Kepler' . .14, 641, 644 

Kirchhoff, - 

Laplac 

Latituci 54a, 589, 

. 600. 
I nature, 117. '05, 769, 770. 

Lehmar.n. 789. 
I^en^t! . 

-01. 

- S8 to 790. 
Libration, 184 



Light. 6 to 15, 425, 550, 725^ 726, 742. 
Limb. 40. I s .;. 5 s >• 

2; oi the apsides, 564; of the 
3 : of the equinoxe 
oi nodes, 181, 195, 1 16, 20a ; of sight) 

Littrou 

Local meridian, 52^. 

Local time, 312, 

Lohse, 

Longitude, 526 to 547, 5S9, 592, 703, 

• 
Lunar cycle, 7; r, 752. 
Lunation, 336, 751? 755- 

Macula, 56. 

Magnesium, 

Magnitude, 81, 686. 

Major axis. 145. 

Mais. 1 1 1 to 201, 334, 345, 359, 729, 733, 

734i 738« 
Mass, to, 4-. So, 92, 605, 606, 654, 662, 

793- 

Material, 5. 

Matter, 5, 13 to 15. 

Maximum of solar spots, 63. 

Mean distance, 147. 

Mean ec.iptic, 549. 

Mean equinox, 545. 

Mean longitude, 577, 787. 

Mean place, 562. 

Mean sun, 575. 

Mean time, 311, 547, 575 to 577, 805. 

Medium of light, 436. 

Mercury, 195, 332, 342, 344, 35^» 360. 

Meridian, 135, 517. 526, 528. 

Meridian circle, 593. 

i > to 250, 277, 802. 
Meton, 751 

Micrometer, 586 to 588, 596. 
Microscope. 5 
Midnight, 312. 
Milky Way, 86 to 89. 
Minimum of solar spots, 63 ; of Algol 
and Mira. - 

M 11. 

Monti,. 

Moon, 20. 21. 121, 172. j~f-> to 1 

Mount.. 

'■' 

I 
movements, mi u 
Mural circles, meridian insti 

ide for determining de- 
clin.i 

Nadir. C 

Nautical time, 315. 



414 



Index. 



Nebulae, 28, 223 to 227, 761. 
Nebular hypothesis, 760 to 764. 
Nebulous stars, 231. 
Neptune, 203, 218 to 221, 334, 748. 
Newcomb, 776, 779, 789. 

Newton, 719 to 725, 747, 749. 

Nicaa, 756. 

Nod :s, 5O3. 

Nodical revolution, 569. 

Normal. 422 to 42 1. 

North. 

Northern tigntS. See Aurora. 

North polar distance, - ? 2-j. 

North star. See Polaris. 

is, 56, 23 1. 
Nutation, 166, 167, 545, 549, 609, 669, 
739i 795- 

( Object-glass, 

Oblique ascension of a star, right ascen- 
sion of the point on the equator which 

it the same time with the star, 
tation, 747. 

< tpera-gla u 
( Opposition, 
( Optical 1 

Orbit, 142, 638, 806. 

Pacific Ocean, chai in cross- 

' I 

■ actic rule-. 

Parallai 

Pa rail 

Parallel 

Paras< 

Parhelion, 

Pencil of ra) 

Pendulum, 129, 160 to 162, I 

7SO, 
Penumbra, 56, 353. 
Perigee, 177. 
Perihelion, 146, 22^, 241, 
Period, 1x9, 750; of Bolai 
Perpendicular, 402^ 415. 
Perspective, 266. 
Perturbations, 170, £41, 660. 
Phasi 

Phosphorescence. 7, 796. 

Photographs, 51, 52. 7 ;. 

Photometers (instruments for measur- 
ing brightness), 686. 

Photosphere, 32, 497. 

Pi (it), 411. 

Picard, 718, 729. 

Plane, 137, 400, 403 ; of the ecliptic or 
of an orbit, 139, 142, 166. 

Planetary nebula. 1 , 224. 

Planets, '28, 85, 107 to 222, 32S to 346, 
669, 670, 787 to 794. 

Points, 392 ; of contact, 422 ; of sight, 

27O, 5!2. 



Polaris, Pole Star, 38, 39, 168, 592, 679 
Poles, 35 to 41, 156, 313, 314, 412, 531. 

Polygon, 418. 

Pole. 

Position of a plane, 401. 

Precedii 

i on, 167, 1S1, 545, 609, & 

5, 790. 
Prime veitH . C92. 

Prism, 431, 43a, 4^9, 501," 502. 
Proctor, 

Projects n, 269, 270, 299. 
Pn mil . 500. 

l'i"I er I —9, 747, 

Ptolemj 

327. 

. 617. 
Quantity of motion, 605, 6io, 611, 659. 

Radius, 1 57, 409. 

I, 148, 568. 

horizon, 264, 310. 
Ray, ; 
I 
Real movement, m, 117, 134. 

K< fit 1 

Refraction. 262, 429, 714, 741. 

montanus, 7 
i I movements, 115, 

Retina, 447, 448. 

;.\ 140, 342 to 345. 

53* 
Ric hei . 

Right angle, right triangle, 420. 
Right ascension, 526, 534, 548 to 550, 

Rising and setting, 124, 520, 691, 692. 
Roemer, 729, 730. 

• 7 2 5- 
Rotation, 33, 43, 60, 160 to 163, 403 to 
408, 

75 2 « 
Satellites, 108, 207 to 210, 216, 219. 220, 
361 to .V<0, 642, C60, 670, 71 

Saturn. 203, 209 to . 4, 3 r °« 

~' r s 7*7> 753. 7 6 3- 
Schmidt, 7S3, 794. 
Schonfeld, 78 
Schwabe 

Scintillation, 106. 
Sea level, 256. 



Index. 



4i5 



Semi.v 

Semidiameter. 15 - ;. 

Shade-. 

Sidereal time, 311. 576, 577) 

I the zodiac , 

• 39°- 
. ;oi to 3°4i 307 to 3»°» 3 2 3* 

:. 519. 

Spectroscope, 66, 488 to 506, 597, 749, 

im, 492, 494, 804. 
Speculum. 
Speed. See K itc. 
Sphere. 

Spider' 

Spot, 5 

1061 12*. 2^3. 2*4, 
2S1 tosl ;)8, 50c, 

61, 680 to 700, 74 

Stereoscopic effect-. \ 187. 

.-.veil, 790, 
-- 

395 to 399- 

s 

180, IS6, to! 

286 to 300, 306 to 322, 370 to 
500, 5 669, 675, 700, 726, 

7)3- 
Sunbeams, - 
Sund 578. 

Sund< ■•_-. 
Sunlic' 

Superior, 199, 32S, 329. 334, 345. 
Surface, 32, 391. 

• • 747- 
2; of freely suspended weights, 

Synod. cal revolution, 335, 336, 5 

: m including both conjunc- 
tions and oppositions. 



I Theodolite, 595. 
Thermopile 

Total eclipse, phase, 30;. 371; reflec- 
tion, 430. 

Trade « 

Trains of meteors, 247. 

Transit, 328, 347, 35S to 361, 5 

• 
Transit Circle, 
Transit instrument, 591. 
TriangK 

577i 75o, 75 x > 

'7) 295. 3oi. 
True time, 317. 
Twilight, 
Twinkling, tot 
Tycho, 194, 71O) 729- 

Umbra, 56, 353. 
Uniform, 120. 
Universe, 16 to 30, 89, 759. 
Up, 

I ranus, 203, 218 to 221, 334, 725. 

Van der Willigen, S04. 

Variable stars, 98, 687, 783. 

Velocity, 600. 

Venus, 196 to 19S, 332, 342, 343, 35^» 73* 

to 733) 753, 801. 
Vernier. 
Vert cal. 252, 663, 666. 

es, 520, 595. 
Visual angle, 452- 
Volcanoes, 173, 189. 

Watch. 579. 
Water, 5, 10. n, 16a, 
Water-docks, 704. 
Weather, 

. 10, 129 to 132, 160, 164, 664, 
665, 

1 
Wet and dry moons, 338. 
Whirlwinds, 70. 
Willow 
Window 
Wolf, - 

"49- 
.4. 



Year, 302 to 304, 573 to 577, 750 to 757, 
800. 



Tables 

. 230. 
Tangent, 422 

■ 
487, S 

ectroscope, 505. 
Temporary stars, 102. 
Tern 330. 332. 

Terrestrial, 4. 



Zenith distance. 5. . 

.. li.^ht, 277. 
Zollnci. 



/ 



.*J 613 



& 



